Portugal | 2016 Czech university of Prague Gao Hongchen Jacey Numerical Simulation of RC Slabs Strengthened with Pre-stressed CFRP Laminates Gao Hongchen Jacey Numerical Simulation of RC Slabs Strengthened with Pre-stressed CFRP Laminates
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Czech university ofPrague
Gao Hongchen Jacey
Numerical Simulation ofRC Slabs Strengthened withPre-stressed CFRP Laminates
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Portugal | 2016
Gao Hongchen Jacey
Numerical Simulation ofRC Slabs Strengthened withPre-stressed CFRP Laminates
NUMERICAL SIMULATION OF RC SLABS STRENGTHENED WITH PRE-STRESSED CFRP LAMINATES
Erasmus Mundus Programme
ADVANCED MASTERS IN STRUCTURAL ANALYSIS OF MONUMENTS AND HISTORICAL CONSTRUCTIONS i
DECLARATION
Name: Gao Hongchen Jacey
Email: [email protected]
Title of the
Msc Dissertation:
Numerical Simulation of RC Slabs Strengthened with Pre-stressed CFRP Laminates
Supervisor(s): Professor Jose Sena-Cruz
Year: 2016
I hereby declare that all information in this document has been obtained and presented in accordance with academic
rules and ethical conduct. I also declare that, as required by these rules and conduct, I have fully cited and
referenced all material and results that are not original to this work.
I hereby declare that the MSc Consortium responsible for the Advanced Masters in Structural Analysis of
Monuments and Historical Constructions is allowed to store and make available electronically the present MSc
Dissertation.
University: University of Minho
Date: 18 July 2016
Signature:
___________________________
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ACKNOWLEDGEMENTS
Firstly, I would like to express my greatest appreciation to the Erasmus Mundus
Scholarship sponsored by the European Commission. The learning opportunities and cultural
immersion offered by the Erasmus Mundus program is deeply cherished. During the 1 year
intensive advanced master program, the vibrant and unique learning experiences in Prague
Czech Republic, Guimaraes Portugal as well as Barcelona Spain, are definitely among the most
precious memories in life.
I would like to express my gratitude to Professor Jose Sena-Cruz for his supervision and
guidance during the course of this dissertation. Moreover, I would like to extend my gratitude
to Professor Miguel Azenha for his assistance and advice for numerical modelling. I deeply
appreciate their support, suggestions and interesting discussions which contribute to my
understanding of the topic. In addition, this study was developed under the auspices of the
FRPLongDur R&P project(POCI-01-0145-FEDER-016900 / FCT PTDC/ECM/112396/2009)
supported by FEDER funds through the POCI Operational Program, the Operational Program
of Lisbon, and National Funds through FCT – Portuguese Foundation for Science and
Technology. The contribution of the experimental work is also acknowledged.
Last but not least, my heartfelt appreciation is dedicated to my family, especially my
mother, for her unconditional love and continuous encouragement. I am deeply grateful for her
unfailing support when making big decisions in life.
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ABSTRACT
In the recent few decades, carbon fiber reinforced polymer materials (CFRP) have
emerged as a common strengthening material for concrete structures due to its advantages such
as high strength and stiffness, lightweight, and corrosion resistant. In addition, CFRP exhibits
excellent fatigue resistance, low creep deformation and low relaxation. One of the most
common strengthening techniques is to apply CFRP as externally bonded reinforcement (EBR).
In this technique, the CFRP laminates are externally bonded to the concrete element usually by
epoxy adhesives to enhance the flexural strength and stiffness. However, one major limitation
of this technique is inefficient mobilization of the high tensile strength of CFRP due to
premature debonding. An innovative improvement to overcome the drawbacks is to apply
prestress to the CFRP laminates in EBR technique for strengthening reinforced concrete (RC)
structures. As a result, the benefits of passive EBR systems are combined with the advantages
associated with external prestressing, thus ensuring greater efficiency for flexural
strengthening. This dissertation aims to better understand the efficiency of prestressed CFRP
laminates for flexural strengthening and to predict different possible failure modes that can
occur by using finite element modelling studies.
A nonlinear FEM study on RC slabs strengthened with prestressed CFRP laminates has
been carried out using the software DIANA®. Prior to the present study, a total of three slabs,
being (i) unstrengthened reference slab; (ii) slab strengthened with un-stressed CFRP by EBR;
and (iii) slab strengthened with prestressed CFRP by mechanical anchorage (MA), were tested
up to failure under a four-point loading configuration. In addition to this, other slabs were also
subjected to sustained loads to assess the long-term structural behavior. All the experimental
work was carried out in the scope of the research project FRPreDur (FCOMP-01-0124-FEDER-
028865). Detailed FEM studies for each slab have been developed to correlate with the
experimental results. Good agreement has been obtained between the experimental and
numerical results. The results highlight the improved performance of the CFRP strengthened
slabs (both un-stressed and prestressed) in terms of lower deflection, crack width delay and
lower crack spacing. In particular, the MA system prevented a premature failure by debonding
and allowed the slabs to support higher ultimate loads and deflections. A greater use of the
CFRP laminate strip tensile capacity was attained with prestressing.
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Based on the existing model, a series of parametric studies have been carried out to
investigate the effects of variation of (i) prestress level; (ii) concrete grade; and (iii) CFRP
laminate geometry, on the flexural behavior of the strengthened slab. An increase in prestress
level provides significant enhancement of load capacity at crack initiation and yielding, and a
significant reduction in mid-span deflection at ultimate failure. The variation of concrete grade
results minimal enhancement in terms of load capacity and mid-span deflection. By increasing
the cross-sectional area of CFRP laminate, the load capacity at crack initiation and yielding is
significantly increased, and such enhancement becomes considerably remarkable at ultimate
failure.
Finally, an exploratory study on modeling of the creep behavior of RC slabs
strengthened with pre-stressed CFRP laminates has been developed. The results seem to be
promising, yielding to the conclusion that the existing numerical tools can simulate with enough
accuracy the strengthening technique studied.
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RESUMO
Nas últimas décadas, o uso de polímeros reforçados com fibras (CFRP - Carbon Fiber
Reinforced Polymer) têm emergido como material de reforço em estruturas de betão existentes,
devido às suas vantagens tais como elevada rigidez e resistência, leveza e resistência à corrosão.
Além disso, os CFRP apresentam excelente resistência à fadiga, baixa deformação por fluência
e de baixa relaxação. Uma das técnicas de reforço mais comumente usadas recorre à aplicação
do reforço (CFRP) nas faces externas dos elementos a reforçar. Esta técnica designa-se por
EBR (Externally Bonded Reinforcement). Nesta técnica, geralmente, os laminados de CFRP
estão fixos externamente ao elemento de betão por intermédio de adesivos de origem epoxídica
para melhorar a sua resistência e rigidez à flexão. No entanto, uma das grandes limitações desta
técnica está associada à deficiente mobilização da resistência à tração de CFRP devido ao
descolamento prematuro deste em relação ao substrato. Melhores resultados podem ser
alcançados com recurso à aplicação de pré-esforço aos laminados de CFRP. Como resultado,
as vantagens da técnica EBR (passiva) são combinadas com as vantagens associadas ao uso de
pré-esforço externo, garantindo assim uma maior eficiência no reforço à flexão. Esta dissertação
tem como objetivo compreender melhor a eficiência de laminados de CFRP pré-esforçados no
reforço à flexão e prever diferentes modos de rotura possíveis que podem ocorrer através de
estudos numéricos com recurso à simulação por intermédio do método dos elementos finitos
(FEM).
Foram efetuadas análises numéricas não lineares baseadas no FEM em lajes de betão
armado reforçadas com laminados de CFRP pré-esforçado com recurso ao software DIANA®.
Previamente ao presente estudo, foram experimentalmente ensaiadas três lajes à flexão: (i) uma
laje não reforçada (considerada laje de referência); (ii) uma laje reforçada com um laminado de
CFRP segundo a técnica EBR; e (iii) uma laje reforçada com um laminado de CFRP pré-
esforçado segundo a técnica EBR e recorrendo a chapas de ancoragem nas extremidades (MA
– Mechanical anchorage). Adicionalmente, lajes foram também submetidos a cargas gravíticas
de modo a avaliar-se o comportamento estrutural de longo prazo. Todo o trabalho experimental
foi realizado no âmbito do projeto de investigação FRPreDur (FCOMP-01-0124-FEDER-
028865). Estudos baseados no FEM de cada laje foram desenvolvidos para as lajes ensaiadas
experimentalmente. Uma boa concordância foi obtida entre os resultados experimentais e os
modelos numéricos. Os resultados relevam a melhoria do uso CFRP (tanto aplicado de forma
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passiva como ativa) em termos de menores deformações, atraso no início da fissuração e
propagação da fissuração. Em particular, o sistema MA impediu a rotura prematura por
destacamento, e permitiu que as lajes pudessem suportar cargas mais elevadas. Adicionalmente,
o pré-esforço permitiu que fossem que fossem atingidas extensões mais elevadas no CFRP.
Com base nos modelos numéricos calibrados, foram realizados estudos paramétricos
para investigar os efeitos da variação (i) do nível de pré-esforço; (ii) da resistência à compressão
do betão; e (iii) da geometria do laminado de CFRP. Um aumento do nível de pré-esforço
proporciona melhoria significativa na carga de início da fissuração e de cedência da armadura
longitudinal, e uma redução significativa da flecha a meio do vão na rotura. A variação da
resistência do betão conduz a melhorias residuais na capacidade de carga e flecha a meio vão
na rotura. Ao aumentar a área da secção transversal do laminado de CFRP, a carga associada
ao início de fissuração e cedência das armaduras longitudinais aumentam de forma
significativa, e este aumento torna se consideravelmente notável na rotura.
Finalmente, foi desenvolvido um estudo exploratório relativo à simulação numérica do
comportamento das lajes reforçadas com laminados de CFRP pré-esforçados devido ao efeito
da fluência. Os resultados aparentam serem promissores, levando à conclusão que as
ferramentas numéricas existentes pode simular com rigor suficiente as técnicas de reforço
estudadas.
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Table of Contents
Chapter 1 INTRODUCTION .................................................................................................. 1
1.1 Carbon Fiber Reinforced Polymers (CFRP) ..................................................................... 1
1.2 CFRP used as Externally Bonded Reinforcement ............................................................ 2
1.3 Objective and Scope ......................................................................................................... 4
1.4 Outline of the Thesis ......................................................................................................... 5
Chapter 2 LITERATURE REVIEWS .................................................................................... 7
2.1 Prestressing Techniques for EBR-CFRP Laminate Systems ............................................ 7
2.1.1 Advantages of Prestressing ........................................................................................ 7
2.1.2 Types of Prestressing ................................................................................................. 8
2.1.3 Anchorage Systems .................................................................................................... 8
2.2 Finite Element Modeling ................................................................................................ 10
2.2.1 Reinforced Concrete Model ..................................................................................... 11
2.2.2 Steel Reinforcement ................................................................................................. 13
2.2.3 CFRP Composites .................................................................................................... 15
2.2.4 Interface Bond Behavior .......................................................................................... 15
2.3 Research Significance ..................................................................................................... 17
Chapter 3 EXPERIMENTAL RESULTS AND ANALYSIS ............................................. 19
3.1 General Information ........................................................................................................ 19
3.2 Specimen Geometry and Test Setup ............................................................................... 19
3.3 Material Characterization ............................................................................................... 21
3.4 Anchorage Procedures .................................................................................................... 22
3.5 Monotonic Load Test ...................................................................................................... 24
3.5.1 Deflection ................................................................................................................. 24
3.5.2 Influence of Prestress ............................................................................................... 25
3.6 Creep Test ....................................................................................................................... 26
3.7 Conclusions ..................................................................................................................... 28
Chapter 4 FINITE ELEMENT MODELLING ................................................................... 29
4.1 Introduction ..................................................................................................................... 29
4.1.1 Model Geometry ...................................................................................................... 29
4.1.2 Element Meshes ....................................................................................................... 31
4.1.3 Element Types .......................................................................................................... 32
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4.1.3.1 Concrete ............................................................................................................ 33
4.1.3.2 Steel Reinforcement .......................................................................................... 33
4.1.3.3 CFRP Laminate ................................................................................................. 34
4.1.3.4 Interface ............................................................................................................ 35
4.1.4 Boundary Conditions ............................................................................................... 36
4.1.5 Loading Conditions ................................................................................................. 36
4.2 Constitutive Material Model Properties ......................................................................... 37
4.2.1 Concrete ................................................................................................................... 38
4.2.1.1 Multi-directional fixed crack model ................................................................. 38
4.2.1.2 Tension cut-off .................................................................................................. 39
4.2.1.3 Tension softening .............................................................................................. 40
4.2.1.4 Shear retention .................................................................................................. 42
4.2.2 Steel Reinforcement ................................................................................................. 42
4.2.3 Carbon Fiber Reinforcement Polymer (CFRP) ....................................................... 44
4.2.4 Concrete-CFRP Interface ......................................................................................... 45
4.3 Prestressing ..................................................................................................................... 46
4.4 Mechanical Anchorage ................................................................................................... 47
4.5 Creep Model ................................................................................................................... 47
Chapter 5 NUMERICAL SIMULATION RESULTS AND DISCUSSIONS .................. 49
5.1 Numerical Simulation for Monotonic Load Tests .......................................................... 49
5.1.1 Load vs Mid-span Deflection ................................................................................... 49
5.1.2 Load vs Mid-span Concrete Strain .......................................................................... 52
5.1.3 Load vs Mid-span CFRP Strain ............................................................................... 54
5.1.4 Load vs Mid-span Longitudinal Steel Strain ........................................................... 55
5.1.5 Crack Patterns .......................................................................................................... 56
5.2 Numerical Simulation for Creep Test ............................................................................ 57
5.2.1 Effects of Temperature and Relative Humidity ....................................................... 58
5.2.2 Loss of Prestress in CFRP ....................................................................................... 59
5.3 Conclusions .................................................................................................................... 60
Chapter 6 PARAMETRIC STUDIES .................................................................................. 61
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6.1 Introduction ..................................................................................................................... 61
6.2 Variation in Prestress Level ............................................................................................ 61
6.3 Variation in Concrete Grade ........................................................................................... 64
6.4 Variation in CFRP Laminate Geometry ......................................................................... 66
6.5 Summary ......................................................................................................................... 68
Chapter 7 CONCLUSIONS AND RECOMMENDATIONS ............................................. 73
7.1 Conclusions from Present Study ................................................................................ 73
7.2 Recommendations for Future Work .......................................................................... 74
References................................................................................................................................ 75
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List of Figures
Figure 1.1 Composition of unidirectional FRP-fibers and matrix ............................................. 2
Figure 1.2 CFRP laminates (left) and CFRP sheets (right)........................................................ 2
Figure 2.1 Schematic Moment-Curvature relationships for an unstrengthened RC element, a
strengthened RC element with an unstressed laminate and a strengthened RC element with a
prestressed laminate [Michels et al., 2016] ................................................................................ 7
Figure 2.2 Different types of prestressing of an existing RC element [El-Hacha et al., 2001] . 8
Figure 2.3 Main procedures for prestressing according to MA and GA systems [extracted
from Michels et al., 2015] ........................................................................................................ 10
Figure 2.4 Uniaxial stress-strain for concrete [Chin et al., 2012] ............................................ 12
Figure 2.5 Tri-linear tensile softening diagram [Sena-Cruz, 2004] ......................................... 12
Figure 2.6 Tensile stress-strain behavior of concrete [Correlas, 2005] ................................... 13
Figure 2.7 Uniaxial constitutive model of the steel reinforcements [Sena-Cruz, 2004] .......... 14
Figure 2.8 Multi-linear stress strain law for steel reinforcement [Chin et al., 2012] ............... 14
Figure 2.9 Simplified multi-linear stress strain relationship for steel reinforcements [Corrales,
2005] ........................................................................................................................................ 14
Figure 2.10 Linear elastic stress strain relation for CFRP laminate ........................................ 15
Figure 2.11 Bond-slip curves from meso-scale finite element simulation and proposed bond-
slip models ............................................................................................................................... 17
Figure 3.1 Specimen geometry and test setup. (All units are in millimeters) .......................... 21
Figure 3.2 Total force versus mid-span deflection .................................................................. 24
Figure 3.3 Total force versus mid-span concrete strain ........................................................... 26
Figure 3.4 Total force versus mid-span CFRP strain ............................................................... 26
Figure 3.5 Testing configuration for the creep test .................................................................. 27
Figure 3.6 Mid-span deflection versus time for MA slab under creep test .............................. 28
Figure 4.1 Geometry details of (a) REF slab and (b) strengthened (EBR and MA) slab (All
units in milimeter) .................................................................................................................... 30
Figure 4.2 Geometrical model of the reference slab (REF) ..................................................... 30
Figure 4.3 Geometrical model of strengthened slab (EBR and MA) ....................................... 31
Figure 4.4 Mesh for reference slab (REF) ............................................................................... 32
Figure 4.5 Mesh for strengthened slabs (EBR and MA) .......................................................... 32
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Figure 4.6 Q8MEM element type [DIANA, 2015] .................................................................. 33
Figure 4.7 Characteristic of truss element [DIANA, 2015] ..................................................... 35
Figure 4.8 L2TRU element type with 2 nodes in a straight line [DIANA, 2015] .................... 35
Figure 4.9 L8IF element typology (left) and displacements (right) ......................................... 36
Figure 4.10 Multi-directional fixed crack model...................................................................... 39
Figure 4.11 Tension cut-off in 2-dimensional principal stress space ....................................... 40
Figure 4.12 Nonlinear tension softening [Hordijk et al., 1987] ............................................... 41
Figure 4.13 Bilinear stress-strain relationship for steel ............................................................ 43
Figure 4.14 The averaged stress-strain relationship for embedded steel reinforcement with
reduced yield envelope [Stevens et al., 1987] .......................................................................... 44
Figure 4.15 The bond-slip model for unidirectional interface element [Lu et al. 2005] .......... 46
Figure 5.1 Load vs mid-span deflection graph comparison for REF slab ................................ 50
Figure 5.2 Load vs mid-span deflection graph comparison for EBR slab ............................... 51
Figure 5.3 Load vs mid-span deflection graph comparison for MA slab ................................. 51
Figure 5.4 Load vs mid-span concrete strain graph comparison for REF slab ........................ 52
Figure 5.5 Load vs mid-span concrete strain graph comparison for EBR slab ........................ 53
Figure 5.6 Load vs mid-span concrete strain graph comparison for MA slab ......................... 53
Figure 5.7 Load vs mid-span CFRP strain graph comparison for EBR slab ............................ 54
Figure 5.8 Load vs mid-span CFRP strain graph comparison for MA slab ............................. 55
Figure 5.9 Load vs mid-span steel strain graph from numerical simulations........................... 56
Figure 5.10 Crack patterns of all slabs from experimental results ........................................... 56
Figure 5.11 Crack patterns from numerical simulation-REF slab ............................................ 57
Figure 5.12 Crack patterns from numerical simulation-EBR slab ........................................... 57
Figure 5.13 Crack patterns from numerical simulation-MA slab ............................................. 57
Figure 5.14 Time evolution of mid-span deflection comparison for creep test ....................... 59
Figure 5.15 Time evolution of mid-span CFRP stress prior to creep test ................................ 60
Figure 6.1 Load vs mid-span deflection graph comparison for variation of prestress levels ... 63
Figure 6.2 Load vs mid-span CFRP strain graph comparison for variation of prestress levels63
Figure 6.3 Load vs mid-span concrete and steel strain graph comparison for variation of
prestress levels .......................................................................................................................... 64
Figure 6.4 Load vs mid-span deflection graph comparison for variation of concrete grade .... 65
Figure 6.5 Load vs mid-span CFRP strain graph comparison for variation of concrete grade 65
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Figure 6.6 Load vs mid-span concrete and steel strain graph comparison for variation of
concrete grade .......................................................................................................................... 66
Figure 6.7 Load vs mid-span deflection graph comparison for variation of CFRP geometry . 67
Figure 6.8 Load vs mid-span CFRP strain graph comparison for variation of CFRP geometry
.................................................................................................................................................. 67
Figure 6.9 Load vs mid-span concrete and steel strain graph comparison for variation of
CFRP geometry ........................................................................................................................ 68
Figure 6.10 Load variation for slabs from parametric studies ................................................. 70
Figure 6.11 Mid-span deflection variation for slabs from parametric studies ......................... 70
Figure 6.12 Stiffness variation for slabs from parametric studies ........................................... 71
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List of Tables
Table 3.1 Experimental program .............................................................................................. 20
Table 3.2 Material characterization (average values) ............................................................... 22
Table 3.3 Main summary of experimental results .................................................................... 25
Table 3.4 Time history of the MA slab for creep test .............................................................. 27
Table 4.1 Summary of number of elements used in the models............................................... 31
Table 4.2 Summary of element types used in the model .......................................................... 32
Table 4.3 Summary of concrete material model properties...................................................... 38
Table 4.4 Coefficient for determining fracture energy [MC 1990] .......................................... 41
Table 4.5 Summary of steel reinforcement model properties .................................................. 43
Table 4.6 Summary of CFRP material model properties ......................................................... 45
Table 4.7 Summary of interface material model properties ..................................................... 46
Table 4.8 Summary of creep model properties ........................................................................ 48
Table 5.1 Main summary of numerical simulation results ....................................................... 60
Table 6.1 Summary of parameter variations for parametric studies......................................... 61
Table 6.2 Main summary of results from parametric studies ................................................... 69
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CHAPTER 1 INTRODUCTION
1.1 Carbon Fiber Reinforced Polymers (CFRP)
In the recent few decades, fiber reinforced polymer materials (FRP) have emerged as a
common strengthening material for concrete structures. FRP is a composite material in the form
of unidirectional or multi-directional strips consisting of two different components: the fibers
and the polymer matrix (Figure 1.1). Carbon (C) and glass (G) are the main types of fibers
composing the fibrous phase of these materials (CFRP and GFRP), whereas epoxy adhesive is
generally used in the matrix phase. The fiber is responsible for carrying the load and has high
strength. The matrix has the following main objectives: (i) to keep the fibers together; (ii) to
protect the fibers against the external actions; (iii) to assure the stress transfer between fibers;
and (iv) in some cases, to serve as a bonding material between the FRP and the component to
be strengthened. The matrix has relatively low strength and transfer load and stress between
fibers [Correia, 2013]. FRP composites are increasingly being considered as an enhancement
to or substitute for civil construction materials, namely concrete and steel. FRP composites are
lightweight, non-corrosive, exhibit high specific strength and specific stiffness. They are easily
constructed and can be tailored to satisfy performance requirements. Due to these advantageous
characteristics, FRP composites have been extensively applied in new construction and
rehabilitation of structures through its use as reinforcement in concrete, bridge decks, and
external reinforcement for strengthening and seismic upgrade [Martin, 2013].
Carbon Fiber Reinforced Polymer composite (CFRP) which contains carbon fibers in
the fibrous phase, has been widely used in construction industry due to the advantages
mentioned above. Additionally, CFRP presents excellent fatigue resistance, low creep
deformation and low relaxation. CFRP for strengthening purpose are commercially available in
two main typologies: laminates and sheets, with different properties depending on the
application (Figure 1.2). The CFRP laminates have unidirectional precured carbon fibers strips
bonded by epoxy matrix while the CFRP sheets have unidirectional or multi-directional mats
of continuous carbon fibers impregnated or bonded with epoxy matrix [Correia, 2013]. Its
ability to increase the flexural, shear or compressive strength of structural concrete members
has been studied and reported in many published literatures, such as Sena-Cruz, 2004; Corrales,
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2005; Michels et al., 2013; Correia et al., 2015. CFRP has been extensively used in flexural and
shear strengthening of beams and slabs, and column confinement strengthening.
Figure 1.1 Composition of unidirectional FRP-fibers and matrix
Figure 1.2 CFRP laminates (left) and CFRP sheets (right)
1.2 CFRP used as Externally Bonded Reinforcement
CFRP has been used in different configurations and techniques to deploy the material
effectively and to ensure long service life of the selected system. One of the most common
strengthening techniques is to apply CFRP as externally bonded reinforcement (EBR). In this
technique, the CFRP laminates are externally bonded to the concrete element usually by epoxy
adhesives to enhance the flexural strength and stiffness. However, the mounting of an
unstressed outer reinforcement (EBR) has the disadvantage of providing a very limited
additional stiffness to the structure under service loads. Several publications revealed that this
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technique is unable to fully mobilize the tensile strength of CFRP material due to premature
debonding [Nguyen et al., 2001; Motavalli et al. 2011; Bilotta et al., 2015]. In most cases, only
20–30 % of the material’s capacity is effectively used [Motavalli et al., 2011], and hence, the
high tensile strength of CFRP is not fully exploited. Moreover, the reinforcing performance of
CFRP materials decreases significantly when exposed to extreme temperature variations
[Pantuso et al., 2000]. In addition, since the CFRP materials used in EBR technique are exposed
to the environment, they are susceptible to damage caused by vandalism and mechanical
malfunctions.
In order to overcome these drawbacks, several improvements have been made with
regards to the EBR technique. Near-surface mounted (NSM) is an emerging strengthening
technique based on bonding CFRP bars or laminate strips into pre-cut grooves on the concrete.
Baschko and Zilch [1999] first published positive experimental results about the use of near-
surface mounted CFRP laminate strips as a strengthening technique. As compared to EBR
system, NSM is more efficient for strengthening existing reinforced concrete (RC) structures
since the debonding phenomenon is less relevant and thus the tensile strength of CFRP materials
can be greater exploited [Barros et al., 2006; Bilotta et al., 2015]. Another great innovation for
strengthening RC structures is to apply prestress to the CFRP laminates in EBR and NSM
systems. The prestressed CFRP for strengthening combines the benefits of passive EBR
systems with the advantages associated with external prestressing [Michels et al., 2013]. Recent
research by Correria et al. [2015] compared the effect of prestressed CFRP laminate strips for
flexural strengthening of RC slabs using different anchorage systems, and revealed that the
prestressed CFRP systems are generally more efficient for flexural strengthening than
unstressed EBR CFRP laminate strips.
Although there have been several researches showing positive findings about the
application of prestressed CFRP laminates as EBR strengthening for RC structures, it should
be also noted that CFRP is brittle in nature. It is elastic until it reaches certain strain and
suddenly fails without warning. Moreover, the behavior of the interface which bonds CFRP and
the strengthening material is difficult to predict. In order to better understand the efficiency of
prestressed CFRP laminates for flexural strengthening and to predict different possible failure
modes that can occur during the experimental phase, finite element modeling (FEM) studies
have been adopted to better envisage the viscoelastic effects experimentally observed.
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1.3 Objective and Scope
The R&D FRPreDur Project (FCT reference - PTDC/ECM-EST/2424/2012), developed
by the University of Minho and EMPA (Swiss Federal Laboratories for Materials Science and
Technology), aiming to assess the short and long-term structural behaviour of concrete elements
strengthened in flexure with prestressed CFRP laminates by mechanical anchorage method. To
study the viscoelastic effects, reinforced concrete slabs were subjected to sustained loads, being
the deformation monitored during a certain period of time. At the end of the long-term structural
behaviour assessment, the slabs were then unloaded and monotonically tested up to failure
[Sena-Cruz, 2015]. Further information about these tests are elaborated in the following
chapters. In order to better understand the results experimentally obtained from the tests up to
failure, as well as the viscoelastic effects experimentally observed, numerical simulations must
be developed.
Consequently, the main objectives of this dissertation are as follows:
(i) To simulate numerically the experimental results of the prestressed slabs tested up to
the failure;
(ii) To simulate numerically the results of the slabs submitted to sustained loads (creep
behaviour);
(iii) To perform parametric studies to analyse the effect of relevant variables, such as
prestressing level, concrete grade and CFRP laminate geometry.
The FEM numerical simulations will be performed in a software-DIANA TNO version
9.6, for the structural analysis by using models based of fracture mechanics. DIANA
(DIsplacement ANAlyzer) is an extensive multi-purpose finite element software package that
is dedicated to a wide range of structural civil engineering problems. The finite element models
in this study are two dimensional, assuming plane stress state.
The scope of this dissertation is specified as follows:
(a) The comparison between numerical and experimental results are mainly in the following
aspects: (i) total applied load versus displacement at the mid-span for the slabs; (ii) total
applied load versus top concrete strain (in compression) at mid-span; (iii) total applied
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load versus CFRP strains at mid-span; (iv) crack patterns; and (v) the total applied load
versus bottom longitudinal steel strains at mid-span for all slabs are presented and
analysed.
(b) Creep test simulation for slab strengthened with prestressed CFRP laminate by MA,
including mid-span deflection and relaxation and viscoelastic effects will be addressed.
(c) The parametric studies involves the following variables: (i) prestressing level at 4%, 6%
and 8%; (ii) concrete grade of C30/37, C35/45 and C40/50; and (iii) CFRP laminate
geometry of L50 × 1.2, L80 × 1.2 and L100 ×1.2. Relevant aspects like cracking,
yielding initiation, load carrying capacity and mid-span deflection will be discussed.
1.4 Outline of the Thesis
Chapter 2 presents literature reviews about prestress techniques for EBR CFRP laminate
systems. In addition, previous research on the constitutive material models of CFRP
strengthened RC structures in finite element analysis will be presented. A brief summary of
research significance of this dissertation will be given at the end of the chapter.
Chapter 3 presents a resume of the R&D Project FRPreDur, with emphasis on the
experimental tests with slabs. Important results such as deflection of the slabs, influence of
prestress level, and crack patterns observed during experiments will be analyzed. A summary
of conclusions which can be drawn from the experimental analysis will be given at the end of
this chapter.
Chapter 4 presents the finite element models developed to simulate the behavior of the
three RC slabs. The selection of constitutive material models for each constituent material,
namely, concrete, steel reinforcement, CFRP and the interface, are elaborated in details. The
properties of these constituent materials are based on the material characterization performed
in the scope of the project. The critical software commands for analysis execution are also
presented.
Chapter 5 presents the results and analysis generated from the finite element modelling.
Comparisons of numerical and experimental results are made mainly in the following aspects:
(i) load vesus mid-span displacement; (ii) load vesus mid-span concrete strains; (iii) load vesus
mid-span CFRP strains; (iv) load vesus mid-span steel strains; and (v) crack patterns. In
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addition, numerical simulation results for creep test is also compared with the experimental
results and analysed.
Chapter 6 presents parametric studies based on the models developed and described in
the previous chapter. The effects of relevant variables are analyzed, such as (i) prestress level;
(ii) concrete grade; and (iii) CFRP laminate geometry. The corresponding numerical results are
presented and analyzed.
Chapter 7 summarizes the conclusions from this study. Some recommendations and
future work are also suggested.
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CHAPTER 2 LITERATURE REVIEWS
2.1 Prestressing Techniques for EBR-CFRP Laminate Systems
2.1.1 Advantages of Prestressing
The Externally Bonded Reinforcement (EBR) technique is the most widely used
strategy in the context of reinforced concrete strengthening. As mentioned in Chapter 1, by
prestressing the CFRP materials attached to the concrete substrate, the advantages of external
prestressing and of the EBR technique are combined and mainly shown in the following aspects
[El-Hacha et al., 2001; Michels et al., 2013]: (i) deflection reduction and acting against dead
loads; (ii) crack widths reduction; (iii) delay in the onset of cracking; (iv) strain relief within
the internal steel reinforcement; (v) higher fatigue failure resistance; (vi) delay in yielding of
the internal steel reinforcements; (vii) more efficient use of concrete and FRP; (viii) reduction
of premature debonding failure; (ix) increase in ultimate load-bearing capacity; (x) increase in
shear capacity. Figure 2.1 illustrates a schematic representation of the moment-curvature (M-χ)
relationship for the three situations, namely the unstrengthened reinforced concrete (RC)
element, a strengthened RC element with unstressed CFRP laminates (EBR) and a strengthened
RC element with prestressed CFRP laminate [Michels et al., 2016]. An enhanced crack, yield,
and ultimate load is shown in terms of an increase in the respective bearing moments ΔMcr, ΔMy
and ΔMu.
Figure 2.1 Schematic Moment-Curvature relationships for an unstrengthened RC element, a
strengthened RC element with an unstressed laminate and a strengthened RC element with a
prestressed laminate [Michels et al., 2016]
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2.1.2 Types of Prestressing
The available methods of prestressing are reviewed and summarized by El-Hacha et al.
[2001]. Generally, there are three methods of prestressing for an existing structure as illustrated
in Figure 2.2. The first technique is known as the cambered beam system, which requires an
initial counter-deflection against the dead-loads by means of hydraulic jacks. Afterwards, the
FRP strip is applied and the structure is thus prestressed due to subsequent releasing of the
initially inflicted deflection. The second method is the use of an external support construction,
in which the equipment for prestressing application is being supported against. The third is the
prestressing against the structure itself. This method requires the previous installation of
supporting elements, such as anchor bolts that are used to fix a hydraulic jack. In most cases,
these temporary elements are removed after the completion of the retrofitting action. This
method is the most common prestressing technique available in the market. Usually, mechanical
anchors are used at the strip ends.
Figure 2.2 Different types of prestressing of an existing RC element [El-Hacha et al., 2001]
2.1.3 Anchorage Systems
It has been recognized that the efficiency of this prestressing technique is directly
depend on the type of anchorage used. Schmidt et al. [2012] reviewed a few anchorage systems
and reported that compared to a bonded anchorage which requires the instant curing of bonding
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agents and needs longer anchorage lengths, a mechanical anchorage is preferred because it is
easy to mount and control the stress through it. Correia et al. [2015] investigated the flexural
behavior of RC slabs strengthened with CFRP strips using two different anchorage systems,
namely mechanical anchorage (MA) and gradient anchorage (GA). For a MA system, the
anchors are fixed to concrete substrate while for a GA system, an accelerated epoxy resin curing
is necessary, followed by a segment-wise prestress force decrease at the strip ends. The main
procedures for prestressing according to MA and GA systems are illustrated in Figure 2.3.
It was reported that both non-prestressed and prestressed EBR strengthening improved
the slabs performance with lower deflection, crack width delay and lower crack spacing. Such
conclusions were also supported by Sena-Cruz et al. [2015] that the CFRP laminate strip is
better exploited when prestressing is used, with slightly higher overall load carrying capacities
for MA than for the GA. In particular, the metallic anchors in the MA system prevented a
premature debonding failure and thus allowed the slabs to support higher ultimate loads and
deflections [Correia et al., 2015]. Sudden strip debonding was observed for GA system, and
this phenomenon was similar to conventional EBR without end-fixation. On the other hand,
MA system experienced progressive strip debonding which allow to precisely capture the
ultimate loading forces [Sena-Cruz, 2015].
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Figure 2.3 Main procedures for prestressing according to MA and GA systems [extracted
from Michels et al., 2015]
2.2 Finite Element Modeling
In the recent few decades, finite element models have increasingly gained popularity in
structural analysis due to its ability to simulate structural behavior of any structures under
various loading conditions. Although a three-dimensional (3D) model is more realistic in most
cases, a two-dimensional (2D) model is often chosen which involves less computational effort
and time. Despite the limitation that a 2D model does not consider the Poisson’s ratio in the
out-of-plane direction, there are several publications accurately simulate the behavior of
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concrete strengthened with CFRP. The relevant works related to this dissertation are
summarized in the following subsections.
2.2.1 Reinforced Concrete Model
To achieve an accurate finite element modelling, it is very critical to adopt the
appropriate constitutive material models. Chin et al. [2012] performed a 2D nonlinear finite
element analysis of RC beams with large openings in shear strengthened with CFRP laminates
using ATENA software, and obtained good correlations between experimental and numerical
results. A rotated smeared crack model was adopted. The equivalent uniaxial law which covers
the complete range of plane stress behaviour in tension and compression was used to derive the
elastic constants as shown in Figure 2.4. The maximum tensile strength is reached linearly,
followed by a nonlinear descending softening law, where a fictitious crack model based on
crack-opening law and fracture energy was used, implying that cracks occur when the principal
stress exceed the tensile strength. The recommendations by CEB-FIP Model Code [1990] has
been adopted to assessing the stress-strain relationship of concrete in compression.
In another research work done by Sena-Cruz [2004], a multi-fixed smeared crack model
was adopted for non-linear behavior of concrete strengthened with CFRP using FEMIX
software. A tri-linear stress-strain diagram, represented in Figure 2.5, is used to simulate the
post-cracking behavior of reinforced concrete element. According to the author, the main
advantage of this approach is the possibility of changing the values of ξ1, α1, ξ2 and α2, thus
providing enough flexibility in order to model the most important aspects of the tension-
stiffening effect.
Corrales [2005] adopted a total strain rotating crack model, which describe the tensile
and compressive behavior of concrete with one stress-strain relationship, to simulate the RC
beams strengthened with CFRP using lateral anchorage strips. It was also concluded that total
strain rotating crack model yielded more accurate representation of concrete behavior than the
smeared crack model. The shear behavior of the concrete after cracking is defined as constant
shear retention for this model, implying that there is no reduction for shear modulus since the
direction of cracks is always perpendicular to the principal stresses. The tensile behavior of
concrete was modelled based on Figure 2.6 shown, with mainly two zones: elastic zone which
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is linearly ascending and softening zone which is nonlinear following the Hordijk et al. [1991]
formulation.
Due to the complexity of non-linearity of concrete, there has been several different
material models adopted for different studies on CFRP strengthened RC beams. According to
these publications, each model is in good agreement with the respective experimental results.
The initial selection of material properties may involve several trials to accurately determine
the relevant parameters.
Figure 2.4 Uniaxial stress-strain for concrete [Chin et al., 2012]
Figure 2.5 Tri-linear tensile softening diagram [Sena-Cruz, 2004]
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Figure 2.6 Tensile stress-strain behavior of concrete [Correlas, 2005]
2.2.2 Steel Reinforcement
For the case of steel reinforcement, on the other hand, it is relatively easier and
straightforward. Sena-Cruz [2004] adopted a uniaxial constitutive model for steel
reinforcements as shown in Figure 2.7 which is an idealized stress-strain relationship obtained
from standard tensile tests. The curve is defined by three points (PT1, PT2 and PT3 in the
figure), composed of four stages: linear elastic stage, yielding plateau, hardening and fracture.
Chin et al. [2012] adopted a similar multi-linear stress strain law (as shown in Figure 2.8) which
consists of four linear lines, defining the same four stages previously mentioned in the earlier
sentence. There is another simplified multi-linear stress strain relationship which consists of
two elastic zones: one defined by the yielding stress of the steel fy and its Young’s modulus Es,
and a second one, also called hardening portion, defined by the ultimate fu and the yielding
stress of the steel [Corrales, 2005]. In many cases, bilinear stress strain relationship (Figure 2.9)
has been adopted by several researchers for steel reinforcement model [Sena-Cruz et al., 2011].
In such case, the yield stress and ultimate stress as well as their corresponding strains are the
necessary parameters to determine the relationship. Perfect bond between steel reinforcements
and concrete is often assumed in the numerical simulation.
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Figure 2.7 Uniaxial constitutive model of the steel reinforcements [Sena-Cruz, 2004]
Figure 2.8 Multi-linear stress strain law for steel reinforcement [Chin et al., 2012]
Figure 2.9 Simplified multi-linear stress strain relationship for steel reinforcements
[Corrales, 2005]
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2.2.3 CFRP Composites
For a unidirectional CFRP laminate in tension, a linear elastic constitutive relation is
assumed as illustrated in Figure 2.10. A rupture point on the stress strain relationship for the
fiber direction defines the ultimate stress and strain of the CFRP. The Young’s modulus is
obtained from the constitutive stress strain relation. [Corrales, 2005; Godat et al., 2010; Sena-
Cruz et al., 2011; Chin et al., 2012; Michels et al., 2014]
Figure 2.10 Linear elastic stress strain relation for CFRP laminate
2.2.4 Interface Bond Behavior
For reinforced concrete members strengthened with CFRP laminates under shear and
flexural, besides conventional concrete failure or CFRP fracture, debonding of CFRP from
concrete substrate is one of the most common failure modes. In fact, debonding can often lead
to overall structural failure. The most significant role of the concrete-CFRP interface is to
transfer the stresses from the concrete to the externally bonded CFRP laminates. The
effectiveness of CFRP strengthening largely depends on this interface bond behavior.
Therefore, to achieve successful strengthening, it is critical to investigate the concrete-CFRP
interface bond behavior and the corresponding models to be applied in simulations.
The bond stress-slip (τ-s) relationship is the fundamental law to describe the interface
behavior of two bonding materials. There are different bond stress-slip law proposed by
different researchers, such as cut-off type, bilinear type and elasto-plastic type [Sato et al., 1997;
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Lorenzis et al., 2001; Chen and Teng, 2001; Lu et al., 2005]. Such divergence indicates the
difficulty in defining a reliable bond stress-slip model for the interface.
Lu et al. [2005] investigated the existing bond-slip models for FRP sheets/plates bonded
to concrete using the results of 253 pull tests on simple FRP-to-concrete bonded joints. In
particular, a set of three new bond-slip models of different levels of sophistications (as shown
in Figure 2.11) proposed in this study, had proven to provide good accuracy for both bond
strength and the strain distribution in the FRP plate. The three bond-slip models shown in Figure
2.11 had been proposed based on the predictions of a meso-scale finite element model, where τ
(MPa) is the local bond (shear) stress, s (mm) is the local slip, τmax (MPa) is the local bond
strength, corresponding to the maximum bond/shear stress experienced by the interface, s0
(mm) is the slip when the bond stress reaches τmax, sf (mm) is the slip when the bond stress
reduces to zero.
Among the three proposed bond-slip models, the bilinear model has been widely
adopted due to its simplification and accuracy [Godat et al., 2010; Chin et al., 2012; Michels et
al., 2014]. According to Lu et al.[2005], the parameters governing the bilinear bond-slip model
are estimated as follows:
𝜏𝑚𝑎𝑥 = 𝛼 × 𝛽𝑤 × 𝑓𝑡 (2.1)
𝑠0 = 0.0195 × 𝛽𝑤 × 𝑓𝑡 (2.2)
𝑠𝑓 =2𝐺𝑓
𝜏𝑚𝑎𝑥 (2.3)
where α = 1.5; 𝑓𝑡 is the tensile strength of concrete; 𝐺𝑓 is the fracture energy given by 𝐺𝑓 =
0.308 × 𝛽𝑤2 × √𝑓𝑡; and 𝛽𝑤 is the width ratio factor given by 𝛽𝑤 = √
2.25−𝑏𝑓/𝑏𝑐
1.25+𝑏𝑓/𝑏𝑐 where 𝑏𝑓 and
𝑏𝑐 is the width of FRP plate and concrete prism respectively.
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Figure 2.11 Bond-slip curves from meso-scale finite element simulation and proposed
bond-slip models
2.3 Research Significance
The research significance of this dissertation is to simulate the experimental results
using DIANA finite element analysis software, highlighting the appropriate constitutive
material models. In addition, the viscoelastic effect of the strengthened RC slab has been studied
via creep analysis. The current work also includes parametric studies, which presents good
predictions for several cases of CFRP laminate strengthened RC slabs without physically
carrying out the experimental work, saving considerable amount of time, effort and cost. The
process of developing these models contributes to the fundamental understanding of finite
element analysis for the author.
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CHAPTER 3 EXPERIMENTAL RESULTS AND ANALYSIS
3.1 General Information
The experiment data used in the present dissertation was carried out in the scope of the
R&D FRPreDur Project (FCT reference - PTDC/ECM-EST/2424/2012). This chapter presents
a summary of the work done, highlighting the important aspects for this dissertation. Additional
information can be found in Sena-Cruz [2015] and Correia et al. [2015].
3.2 Specimen Geometry and Test Setup
The experimental program was composed of three reinforced concrete (RC) slabs. One
slab was used as controlled specimen (REF). One slab was strengthened with a simple CFRP
laminate strip according to the EBR technique without any prestressing (EBR). The remaining
slab was strengthened with one externally bonded prestressed CFRP laminate strip with a
mechanical anchorage (MA). After casting the specimens and before proceed with the
application of the CFRP reinforcement, the concrete region of the three slabs where the CFRP
was installed were treated by means of sand blasting. The main aim of surface treatment was to
remove the weak concrete layer and expose the aggregates to the substrate to ensure sufficient
bonding between concrete and CFRP. The cross-sectional geometry of CFRP was 50 mm by
length and 1.2 mm by thickness. The initial strain and prestreesing force applied to the CFRP
were shown in Table 3.1 below.
The geometry of the specimens and test configuration are shown in Figure 3.1. All slabs
have a total length of 2600 mm, being the cross-section of width 600 mm and height 120 mm.
The upper and lower longitudinal inner reinforcement is composed of three steel bars with a
diameter of 6 mm (3Ø6) and five steel bars of a diameter of 8 mm (5Ø8), respectively.
Transverse reinforcements were installed by means of steel stirrups with a diameter of 6 mm
(Ø6) spaced at 300 mm. The length of CFRP laminate strips used were 2200 mm.
Monotonic tests up to failure were performed using a four point bending configuration
in order to access the service and ultimate behavior of all slabs, being the shear span equal to
900 mm. The two supports were located at 100 mm away from the extreme ends of the slab.
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Five linear variable differential transducers (LVDT1 to LVDT5) were used to record the
deflection along the longitudinal axis of the slab; 3 strain gauges (SG1 to SG3) to measure the
strain in the laminate and concrete; and 1 load cell to measure the applied load (F). Figure 3.1
shows the position of each LVDT: three in the pure bending zone with the range of ±75 mm
and a linearity error of ±0.10% and two between the supports and the applied load points with
a range of ±25 mm and the same linearity error. The load cell used has a maximum measuring
capacity of 200 kN and a linear error of ±0.05%. Two different strain gauge types were used:
(i) two TML BFLA-5-3 strain sensors (SG1 and SG2) glued on the laminate surface at the mid-
span and at the force application point; and, (ii) one TML PFL-30-11-3L strain sensor (SG3)
for the measuring the concrete strain in the mid-span. All tests were carried out with a servo-
controlled equipment under displacement control at a rate of 1.2 mm/min. The crack width
evolution was measured during the test through a handheld USB microscope which consists of
the VEHO VMS-004 D microscope, with a native resolution of 640 × 480 pixels and
magnification capacity up to 400×. In this experimental program, the crack width acquisition
was done with a magnification factor of 20× up to predefined applied load.
It should be highlighted that, usually, in reality for existing structures cracks already
exist at the point of the CFRP application. Consequently, the present experimental program
does not totally reproduce the major part of the existing structures that require upgrading.
However, critical aspects such as post-cracking behavior, yielding of the longitudinal
reinforcements, ultimate load and failure modes can be well-captured by the present
experimental program. Hence, the structural behavior of the slabs can be considered
representative of the expected real behavior. Additionally, it is also possible to evaluate the
effect of the CFRP prestressing on crack initiation from this experiment.
Table 3.1 Experimental program
Specimen
Laminate
geometry [mm2]
Initial strain,
εfp [×10-3]
Prestress force
[kN]
Anchorage
system
REF - - - -
EBR 50 × 1.2 0 - -
MA 51 × 1.2 4.23 41.6 MA
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Figure 3.1 Specimen geometry and test setup. (All units are in millimeters)
3.3 Material Characterization
The mechanical properties of the materials involved in the experimental program,
namely concrete, steel, CFRP laminate strip and epoxy adhesive, were being evaluated.
Concrete characterization included evaluation of the modulus of elasticity (Ec) and compressive
strength (fc) through LNEC E397-1993 [1993] and NP EN 12390-3 [2011] recommendations,
respectively. Six cylindrical specimens with 300 mm of height and 150 mm of diameter were
used. Table 3.2 shows the results obtained on the testing day. The average compressive strength
of concrete was about 40 MPa.
The tensile properties of the steel reinforcement were assessed throughout the NP EN
ISO 6892-1[2012] standard. A minimum of three specimens were used for each bar type. Table
3.2 includes the Young's modulus (Es) as well as the yield (fy) and ultimate (fu) strengths
obtained from the tensile tests. The average value of the modulus of elasticity was about 207
GPa and 235 GPa for the upper and lower longitudinal steel reinforcement, respectively. The
steel of the longitudinal bars and stirrups has a denomination of A400 NR SD according to the
NP EN 1992-1-1 [2010].
The CFRP laminate strips used in the experimental work consists of unidirectional
carbon fibres held together by an epoxy vinyl ester resin matrix. Typically, this type of CFRP
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laminate presents smooth external surface and the fibre volume content is higher than 68%
[S&P, 2014]. The modulus of elasticity (Ef) and tensile strength (ff) were obtained from tests
performed according to the ISO 527-5 [1997] standard. The values presented in Table 3.2 are
based on the average of six samples and yielded to a mean Young's modulus that varied between
164 GPa and minimum tensile strength of 2375 MPa.
The epoxy adhesive, produced by the same supplier as for the CFRP laminate, was used
as bond agent to fix the reinforcements to the concrete substrate. This epoxy adhesive is a
solvent free, thixotropic and grey two-component (Component A resin, light grey colour and
Component B hardener, black colour). The mixing ratio (A:B) is 4:1 by weight. According to
the manufacturer, after mixing the two components, the homogenized compound density is 1.70
to1.80 g/cm3 and has the following mechanical properties [S&P, 2013]: compressive strength
>70 MPa; tensile E-modulus >7.1 GPa; shear strength >26 MPa; adhesive tensile strength to
concrete or CFRP laminate >3 MPa (after 3 days of curing at 20 ºC). After 7 days of curing at
22 ºC, a Young modulus of 7.7 GPa (CoV 3.1%) and a tensile strength of 20.7 MPa (CoV 9.9%)
were obtained [Correia et al., 2015].
Table 3.2 Material characterization (average values)
Concrete Ec [GPa] fc [MPa]
30 (n.a) 40.2 (0.7%)
Steel
Diameter [mm] Es [GPa] fy [MPa] ft [MPa]
6 206.9 (0.4%) 519.4 (6.1%) 670.2 (5.1%)
8 235.1 (4.6%) 595.9 (4.1%) 699.0 (2.1%)
CFRP Geometry [mm2] ECFRP [GPa] ff [MPa]
50 ×1.2 164 (3.1%) 2374.9 (2.5%)
Note: the values in the parentheses are the corresponding coefficients of variation (CoV).
3.4 Anchorage Procedures
The procedures for installation of mechanical anchorage consists of the following main
steps [Michels et al., 2015]:
(i) The first step is the surface preparation of concrete substrate where the strip is applied.
In this experiment, sandblasting method was used for concrete surface preparation.
Afterwards, compressive air was used to clean the treated region of the slab;
(ii) Several holes are drilled to accommodate temporary and permanent bolt anchors. Six
M16 8.8 permanent bolt anchors are used to fix each steel anchorage plate. HIT-HY
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200-A® chemical bond agent was used to fix the bolts to concrete. Then, aluminum
guides are placed in the right position to guide and fix the clamp units;
(iii) The clamp units are placed in-between the guides at each extremity of the slab;
(iv) The epoxy adhesive is prepared according to the requirements included in producer's
technical datasheet and the CFRP laminate strip is cleaned with a solvent. Then, the
adhesive is applied on the surface of the CFRP laminate as well as on the concrete
surface region in contact with the laminate. A minimum of 2 mm of thickness of epoxy
was used. The CFRP laminate strip is then placed in its final position and slightly
pressed against the concrete substrate;
(v) The clamping units are closed and a dynamometric key is used to tighten the screws of
the clamp units with a torque of 170 N m;
(vi) Anchor plates are slightly grinded with sandpaper and cleaned with a solvent before
they are installed in their predefined location. The anchor plates of 270 mm × 200 mm
× 10 mm, made of hard aluminum, have 6 holes of 18 mm diameter to accommodate
the 6 permanent bolt anchors of 16 mm of diameter;
(vii) The aluminum frames are then placed on their predefined locations and fixed against
the concrete with the anchors in order to accommodate the hydraulic cylinder for the
application of the prestressing;
(viii) Finally, using a manual hydraulic pump, the prestress is applied to the CFRP laminate
strip.
After CFRP is being prestressed, a torque of 150 Nm in each bolt anchor of the anchor
plates (with a geometry of 270 mm × 200 mm × 20 mm) is being applied to increase the
confinement level in this region and hence reducing the probability of the CFRP laminate
sliding at the ends. Subsequently, by using additional fixing screws mounted in-between the
frame and the clamp units, the prestressing system is being blocked in order to avoid prestress
losses during the curing of the epoxy. The strengthening application is concluded after
approximately 24 h, since after this time span the epoxy reaches a degree of curing at about
90% [Fernandes et al., 2015]. In the end, the equipment is removed (fixing screws, clamp units,
guides and aluminum frames) and the temporary anchors and CFRP laminate outside of the
anchor plates are cut off.
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3.5 Monotonic Load Test
3.5.1 Deflection
The relationship between the applied force and the mid-span deflection was monitored
and the results are shown in Figure 3.2. The strengthening (both non-prestressed and
prestressed) increased the stiffness of the RC slab and CFRP strip composite system, and
consequently reduced the deflection for the same applied load as compared to the controlled
RC slab. This proves that CFRP strengthening is an effective method to enhance the flexural
strength against deflection.
It can be observed from Table 3.3 which summarizes the key results that, prestress did
not significantly change the stiffness of the elastic phase (KI). However, substantial differences
were observed in the stage after the crack initiation: firstly, cracking (ẟcr, Fcr) and steel yielding
(ẟy Fy) were delayed when compared with the non-prestressing specimens; and the stiffness
after cracking (KII) was higher in the strengthened slabs.
Figure 3.2 Total force versus mid-span deflection
0
20
40
60
80
0 20 40 60 80 100 120
Tota
l lo
ad, F
[kN
]
Mid-span displacement,ẟ [mm]
REFEBRMA
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Table 3.3 Main summary of experimental results
Specimen
Stiffness Crack
Initiation
Yielding Ultimate
KI KII ẟcr Fcr ẟy ϕy Fy ẟmax Fmax ϕmax εfmaxc
[kN/mm] [kN/mm] [mm] [kN] [mm] [10-3m-1] [kN] [mm] [kN] [10-3m-1] [10-3]
REF 11.10 0.92 0.71 7.88 18.90 - 24.54 100.0a 28.07b - -
EBR 12.49 1.13 0.68 8.49 25.87 43.88 37.05 40.69 43.98 71.34 7.56
MA 9.82 1.31 1.82 17.87 26.88 44.81 50.58 84.78 67.46 77.26 14.76
Note: a The slab reached maximum pre-defined deflection without failing
b Values for mid-span deflection of 100 mm
c The maximum CFRP strain did not necessarily occur at the mid-span
3.5.2 Influence of Prestress
The overall behavior of the prestressed specimens was considerably more satisfying
than the un-prestressed ones in terms of ductility and load carrying capacities. Prestressing
clearly improved the cracking and yielding initiation, stiffness and load carrying capacity. Even
though the stiffness at the uncracked stage (KI) was similar (prestressed versus un-prestressed)
mainly due to the low level of strengthening ratio and level of prestrain that has been used, the
cracking load was significantly higher. Similar observations can be made for the cracked stage
(before yielding initiation). The load carrying capacity of prestressed slabs increased when
compared with the unprestressed specimen.
Figure 3.3 and 3.4 illustrate the evolution of the concrete and CFRP strains at mid-span
with the total force, respectively. It shows a higher ultimate strain in the concrete for the
prestressed specimens. Consequently, it can be stated that prestressing the CFRP laminates not
only improved the slabs overall performance but also assured a better use of the materials. It
should be also referred that a greater portion of the CFRP tensile capacity was mobilized with
the prestress (see Figure 3.4 and Table 3.3): the strain at the ultimate load (Fmax) for the MA
was 95% higher than the results observed on the EBR.
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Figure 3.3 Total force versus mid-span concrete strain
Figure 3.4 Total force versus mid-span CFRP strain
3.6 Creep Test
During the experiment program, creep tests were carried out on the MA slabs to
investigate its long-term structural behavior under sustained load. The loading configuration is
illustrated in Figure 3.5 and the time history of the slab is summarized in Table 3.4. A sustained
0
10
20
30
40
50
60
70
0 1 2 3 4 5
Tota
l l
oad
, F
[kN
]
Mid-span concret strain, εc [×10-3]
REFEBRMA
0
10
20
30
40
50
60
0 5 10
Tota
l fo
rce,
F [
kN
]
Mis-span CFRP strain,εCFRP [×10-3]
EBR
MA
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load of 20 kN was applied on 17-Dec-2014 and only the mid-span deflection was measured
against time until the end of the creep test on 1-Sep-2015. It should be noted that the ambient
temperature was not controlled for the first 350 hours of the creep test. The slab was only
submitted to the controlled environment (20ºC and 50% RH) after 350 hours from the beginning
of the creep test.
The mid-span deflection of the slab versus time during creep test is shown in Figure 3.6.
The instantaneous mid-span displacement of the MA slab after the load was being applied was
approximately 6 mm. Then the mid-span deflection gradually reached a constant value of
approximately 11 mm at about 190 days of creep test. The mid-span deflection after 190 days
remained almost constantly at 11 mm until the end of the creep test.
Figure 3.5 Testing configuration for the creep test
Table 3.4 Time history of the MA slab for creep test
Date Event Age [day]
11-Apr-2014 Casting concrete slab 0
9-May-2014 Material characterization 28
28-Jun-2014 Strengthening/Prestressing 78
17-Dec-2014 Beginning of creep test 250
1-Sep-2015 Unloading 507
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Figure 3.6 Mid-span deflection versus time for MA slab under creep test
3.7 Conclusions
The main objective of the experiment is to assess the service and ultimate behavior of
the RC slab strengthened with prestressed CFRP laminate strips according to EBR techniques.
In addition, creep test aims to investigate the long-term behavior of the strengthened slab under
sustained load. From the work carried out and described in the present chapter, several
conclusions could be drawn based on the experimental results.
At service level, strengthening with CFRP (both prestressed and non-prestressed)
improved the performance of the slabs in terms of lower deflection, crack width delay and lower
crack spacing. In addition, the metallic anchors composing the MA system prevented a
premature failure by debonding and allowed the slabs to support higher ultimate loads and
deflections. A greater use of the CFRP laminate strip tensile capacity was attained when
prestressing was applied to the CFRP laminates. The average ultimate strain on the CFRP
laminate increased by 74% with prestressing for the slabs tested.
0
2
4
6
8
10
12
14
0 50 100 150 200 250 300
Mid
-span
Dis
pla
cem
ent
[mm
]
Time [Day]
MA
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CHAPTER 4 FINITE ELEMENT MODELLING
4.1 Introduction
Finite element simulation of the slabs is carried out using the commercial finite element
software DIANA 9.6, which is well known for modeling concrete structures due to its wide
range of concrete materials models and advanced numerical tools. The non-linear mechanisms
that are considered in modeling are cracking of concrete, yielding of reinforcement and the
debonding (or failure) of the CFRP laminate. All the finite element models in this study are two
dimensional assuming plane stress state. iDIANA is mainly used for pre-processing and post-
processing of the models, while Command Box is used to run the analysis.
4.1.1 Model Geometry
Three reinforced concrete (RC) slabs were being tested under four-point bending test
configuration. One RC slab was used as controlled specimen (REF). One RC slab was
strengthened with a simple CFRP laminate strip according to the EBR technique without any
prestressing (EBR). The remaining slab was strengthened with one externally bonded
prestressed CFRP laminate strip with a mechanical anchorage (MA). All slabs have a total
length of 2600 mm, the rectangular cross section of width 600 mm and height 120 mm. The
CFRP laminates is located at 200 mm away from two ends, having an effective length of 2200
mm (Figure 4.1). The detailed geometry about the slabs are descripted in Chapter 3 section 3.2
Specimen geometry and test setup.
Due to the symmetry of the test configuration, half of the slab is used for numerical
simulation, reducing the computing time considerably. Figure 4.2 shows the geometrical model
of REF slab, while Figure 4.3 shows the ones for the case of slabs with EBR and MA
respectively. Note that for the strengthened slabs (EBR and MA), there is a 2mm thickness of
interface between the bottom surface of concrete slab and CFRP.
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Figure 4.1 Geometry details of (a) REF slab and (b) strengthened (EBR and MA) slab (All
units in milimeter)
Figure 4.2 Geometrical model of the reference slab (REF)
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Figure 4.3 Geometrical model of strengthened slab (EBR and MA)
4.1.2 Element Meshes
Rectangular finite element of 25 mm × 15 mm were used for modeling the concrete
component of all slabs. The number of elements used to mesh concrete and steel reinforcement
are kept constant. Table 4.1 shows the number of elements used to model each constitutive
material of the model for the three slabs.
Table 4.1 Summary of number of elements used in the models
Number of elements
REF EBR MA
Concrete 416 416 416
Steel reinforcement 124 124 124
CFRP laminate - 44 44
Interface - 44 44
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Figure 4.4 Mesh for reference slab (REF)
Figure 4.5 Mesh for strengthened slabs (EBR and MA)
4.1.3 Element Types
There are a total of four different element types used in this study. The selection of
element type was based on various circumstances, such as mesh typology, boundary conditions
and property assignment. Table 4.2 summarizes all the element types used in the model. The
details of element type for each material will be elaborated in the following subsections.
Table 4.2 Summary of element types used in the model
Material Element type DIANA syntax
Concrete Quadrilateral isoparametric plane stress
element QU4 Q8MEM
Steel Embedded reinforcement REINFORCE BAR
CFRP laminate Regular truss element BE2 L2TRU
Interface Double line element 2+2 nodes IL22 L8IF
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4.1.3.1 Concrete
Concrete is discretized using quadrilateral element QU4. QU4 is defined by 4 nodes
connected by 4 straight lines within a specified element. The element type for the model is
Q8MEM as illustrated in Figure 4.6. The Q8MEM element is a four-node quadrilateral
isoparametric plane stress element. It is based on linear interpolation and Gauss integration
[DIANA, 2015]. The polynomial for the displacements ux and uy can be expressed as
𝑢𝑖(𝜉, 𝜂) = 𝑎0 + 𝑎1𝜉 + 𝑎2𝜂 + 𝑎3𝜉𝜂
Typically, this polynomial yields a strain εxx which is constant in x direction and varies linearly
in y direction and a strain εyy which is constant in y direction and varies linearly in x direction.
For constant shear, the Q8MEM element yields a constant shear strain γxy over the element
area. By default DIANA applies 2 × 2 [nξ = 2, n𝜂 = 2] integration, 1 x 1 is a suitable option for
which DIANA applies a stabilization procedure to avoid zero-energy modes. Schemes higher
than 2 × 2 are not suitable.
Figure 4.6 Q8MEM element type [DIANA, 2015]
4.1.3.2 Steel Reinforcement
All the steel reinforcement are modeled as embedded reinforcement which does not
allow relative slip between steel and concrete. They are represented as lines in a two-
dimensional finite element model. In DIANA, the space occupied by embedded reinforcements
is ignored. The embedded reinforcements do not contribute to the weight of the whole model.
Since embedded reinforcements do not allow relative slip, they have no degree of freedom on
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their own. In addition, the strains in the reinforcements are computed from the displacement
field of the concrete element. This implies that there is perfect bond between the reinforcement
and concrete.
In this study, there are two types of steel, with diameters of 6 mm (Ø6) and 8 mm (Ø8),
being used. Ø6 steel bars are used as upper longitudinal reinforcement and shear reinforcement,
while Ø8 steel bars are used as bottom longitudinal reinforcement. The material
characterization and detailing information are elaborated in details earlier in Chapter 3. These
steel reinforcement bars are generated by locating the start and end points within the concrete
element using global coordinates. Subsequently, the steel reinforcement are assigned with their
respective material properties.
4.1.3.3 CFRP Laminate
In this dissertation, regular truss element is used to model CFRP laminates. In DIANA,
there are three types of truss elements available: regular, enhanced and cable elements.
Enhanced and cable elements are suitable for higher degree of freedom perpendicular to the bar
or element axis as shown in Figure 4.7. Moreover, the deformation of truss elements can only
be the axial elongation Δl, without bending nor shear deformation. According to DIANA
manual, truss elements are bars which must fulfill the condition that the
dimensions d perpendicular to the bar axis are small in relation to the length l of the bar as
shown in Figure 4.7. In the experiment, the thickness of the slab is 120 mm and it is considered
rather small in relation to the length of CFRP laminates are 2200 mm for the whole slab (or
1100 mm for half the slab). In addition, CFRP laminates are bonded to the bottom surface of
the slabs, either as externally bonded reinforcement (EBR), or by means of mechanical
anchorage (MA), there is no degree of freedom in the direction perpendicular to the CFRP
laminates. Therefore, regular truss element is adopted to model CFRP.
The truss element types are represented as lines in DIANA. In this study, the L2TRU is
used as element type for CFRP (Figure 4.8). L2TRU has linear interpolation functions for the
displacement field ux, meaning that there are only two nodes along the line for regular truss
element. This element type yields a constant strain along the bar axis.
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Figure 4.7 Characteristic of truss element [DIANA, 2015]
Figure 4.8 L2TRU element type with 2 nodes in a straight line [DIANA, 2015]
4.1.3.4 Interface
The interface elements describe the interface behavior in terms of a relation between the
normal and shear tractions and the normal and shear relative displacements across the interface.
There are several typical applications of structural interface elements, such as elastic bedding,
bond-slip along reinforcement, friction between surfaces and masonry joints. According to
DIANA 9.6 user manual [2015], there are four types of structural interface elements available
with respect to shape and connectivity: nodal interface elements, line interface elements, line-
solid connection interface element and plane interface elements. In this study, line interface
element which is to be placed between truss element and concrete plane stress element in a two-
dimensional model, is most suitable to model the concrete-FRP interface.
Since the element type used for CFRP laminate has two nodes in a straight line, the
element type for concrete-CFRP interface should match the number of nodes per line with that
of CFRP laminate. Therefore, L8IF which is an interface element between two lines in a two-
dimensional configuration is chosen as the interface element type (Figure 4.9). For L8IF
interface element, the local xy axes for the displacements are evaluated in the first node
with x from node 1 to node 2.
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Figure 4.9 L8IF element typology (left) and displacements (right)
4.1.4 Boundary Conditions
All slabs under four-point bending test were simply supported. Due to the symmetry
effect of loading and slab geometry, only half of the actual slab was modeled. In the model, the
left support provides constrain of translation in y-direction, located at 100 mm from the slab
end. Roller support is provided at the mid-span to restrict translation in x-direction and allow
translation in y-direction as shown in Figure 4.2 and 4.3.
4.1.5 Loading Conditions
The actual four slabs were subjected to two concentrated static loads applied at 600 mm
apart (as shown in Figure 4.1). In the model which is half of the actual slab, the loading point
is located at 300 mm away to the mid-span. During the experiment, all tests were carried out
with a servo-controlled equipment under displacement control at a rate of 1.2 mm/min. The
ultimate load capacity of the slabs and displacement at mid span were measured. The
experimental results and analysis were elaborated in details in Chapter 3. It was observed from
the experiment that the maximum mid-span deflection for slabs were approximately 100 mm.
In order to simulate the test condition, a prescribed displacement of 100 mm was assigned as
the load condition to the model.
In a non-linear analysis for a finite element model, the load is not applied all at once,
but it is incrementally applied in a specified number of “load steps”. Load steps are explicitly
determined by the user in the command file. In each load step, a system of nonlinear equations
are being solved. At the end of each incremental solution, the global stiffness matrix is modified
to take into account the nonlinear behavior of the materials before going to the next increment.
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Regular Newton-Raphson iterative solution method is used to obtain convergence between
internal and external forces in the model and then the displacement vectors.
The load steps applied in the model are not of the same magnitude. This is due to the
fact of nonlinear behavior of the materials used, mostly concrete. From the experimental load-
displacement curve result, there are a few distinguished nonlinear behavior observed. These
marked points are corresponding to mechanical behaviors of the slabs during testing, such as
first crack, steel yielding, interface debonding and concrete crushing and so on. The load step
size is significantly reduced around these parts in order to obtain representative behaviors and
avoid divergence.
Once the analysis is complete, the load-step increment curve can be obtained from the
left support element node. The displacement-step increment curve can be obtained from the
loading point element node. The total load applied to the slab and the corresponding
displacement can therefore be plotted through force-displacement graph. Moreover, total
applied force versus the bottom longitudinal steel reinforcement strain at mid-span is also
captured for all four slabs. This information enables us a better understanding of the tensile
behavior and thus the maximum tensile strain experienced by the bottom longitudinal steel
reinforcement which could not be easily measured during experimental process. In addition,
the total applied force versus top concrete strain at mid-span is monitored and compared with
experimental results for all four slabs. The total applied force versus CFRP strain at mid-span
is also captured and compared with experimental results for all slabs except for the REF slab.
Finally, the numerical crack patterns obtained at the final step are mapped with the ones
observed during the experiment.
4.2 Constitutive Material Model Properties
In a finite element analysis, one of the most difficult task is probably to accurately
predict the material models to be used, especially for the case of nonlinearity of the material.
There are a total of four different materials used in the finite element model, namely: concrete,
steel reinforcement, CFRP laminates and CFRP-concrete interface. In this study, there are
mainly two procedures to evaluate and define the respective material models. Firstly, the basic
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material properties can be obtained from experimental testing as presented in Chapter 3. In
addition, empirical equations or recommendations from published literatures have been adopted
as well. In some cases which is difficult to get an accurate behavior of the material, some
assumptions have to be made and will be discussed in details in the following subsections.
4.2.1 Concrete
Concrete is a heterogeneous, cohesive-frictional material and exhibits non-linear
inelastic behavior under multi-axial stress states in real life. Concrete contains many micro-
cracks, especially at the interface between aggregates and mortar, even before application of
external loads. There are many theories proposed in the literatures to predict the concrete
behavior in nonlinear analysis. One of the most challenging tasks in a finite element analysis
is to simulate concrete in a nonlinear analysis. Table 4.3 summarizes the material model adopted
for concrete in this study. The following subsections will explain in details about each property.
Table 4.3 Summary of concrete material model properties
Property Remarks DIANA syntax
Young’s modulus, Ec 30 GPa YOUNG 3.00E+4
Poisson ratio 0.2 POISON 0.2
Compressive strength, 𝑓𝑐𝑚 40 MPa -
Tensile strength, 𝑓𝑡 2 MPa -
Crack model Multi-directional fixed crack -
Tension cut-off Constant CRACK 1
Tension softening Hordijk et al,. TENSIO 5
Fracture energy, Gf 0.07 N/mm GF 0.07
Crack bandwidth, h 30 mm CRACKB 30
Shear retention Full shear retention TAUCRI 0
4.2.1.1 Multi-directional fixed crack model
In this study, multi-directional fixed smeared crack model is used for concrete under
nonlinear analysis. In a multi-directional fixed smeared crack model, cracking is specified as a
combination of tension cut-off, tension softening and shear retention. The fundamental feature
of the smeared crack model is the decomposition of the total strain ε into a concrete
strain εco and a crack strain εcr as
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ε = εco + εcr (4.1)
An advantage of such total strain decomposition is that it allows for a further sub-decomposition
of the crack strain into its contributors from a series of multi-directional cracks that
simultaneously occur as
εcr = ε1cr + ε2
cr + …… (4.2)
where ε1cr is the global crack strain increment owing to a primary crack, while ε2
cr is the global
crack strain increment owing to a secondary crack and so on. The sub-decomposition of the
crack strain εcr gives the possibility of modeling a number of cracks that simultaneously occur.
The significant feature of this multi-directional fixed crack concept is that a stress σi and
strain εicr exists in the n -t coordinate system that is aligned with each crack i as illustrated in
Figure 4.10. Whenever the angle of inclination between the existing crack(s) and the current
direction of principal stress exceeds the value of a certain threshold angle α, a new crack is
initiated. As such, a system of non-orthogonal cracks is implied as pioneered by de Borst and
Nauta [1985].
Figure 4.10 Multi-directional fixed crack model
4.2.1.2 Tension cut-off
Tension cut-off is one factor that governs the crack initiation and propagation. There
are two tension cut-off criteria available in DIANA: constant and linear, as shown in Figure
4.11. Tension cut-off criterion implies that cracks occur when the principal tensile stress
violates the maximum stress condition. For instance, constant stress cut-off implies that a crack
arises if the major principal tensile stress exceeds tensile strength ft which is the controlling
strength to determine crack initiation. A linear stress cut-off implies that a crack arises if the
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major principal tensile stress exceeds the minimum of ft and ft (1 + σlateral /fc), with σlateral the
lateral principal stress and fc the compressive strength.
In this study, a constant stress cut-off criteria has been adopted. The tensile strength ft
was not experimentally determined, but estimated based on formulations recommended by
CEB-FIB [1990] as follows:
𝑓𝑐𝑡,𝑚𝑒𝑎𝑛 = 0.3 × 𝑓𝑐𝑘
23 (4.3)
where 𝑓𝑐𝑘 = 𝑓𝑐𝑚 − 8𝑀𝑃𝑎, with 𝑓𝑐𝑚 equals to 40 MPa as determined from the experiment.
However, when the tensile strength ft estimated from Equation (4.3) which is about 3 MPa was
used as the stress cut-off criteria, it has been noted that the overall behavior of the model has
been overestimated. Due to this observation, a tensile strength value of 2 MPa has been adopted
in the analysis.
Figure 4.11 Tension cut-off in 2-dimensional principal stress space
4.2.1.3 Tension softening
The relation between the crack stress 𝜎𝑛𝑛𝑐𝑟 and the crack strain 𝜀𝑛𝑛
𝑐𝑟 in the normal
direction can be written as a multiplicative relation
𝜎𝑛𝑛𝑐𝑟 (𝜀𝑛𝑛
𝑐𝑟 ) = 𝑓𝑡 × 𝑦 (𝜀𝑛𝑛
𝑐𝑟
𝜀𝑛𝑛.𝑢𝑙𝑡𝑐𝑟 ) (4.4)
in which ft is the tensile strength and 𝜀𝑛𝑛.𝑢𝑙𝑡𝑐𝑟 the ultimate crack strain. The general
function y represents the actual softening diagram. In DIANA both the tensile strength and
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ultimate strain may be a function of temperature, moisture concentration or maturity. Therefore
the development of tensile strength and fracture energy in time can be simulated.
In this study, among all eight available tension softening models in DIANA, a nonlinear
tension softening according to Hordijk et al.[1987] , which has been adopted by many
researchers [Chin et al., 2012; Correlas, 2005], is used. This model proposed an expression for
the softening behavior of concrete which also results in a crack stress equal to zero at a crack
strain 𝜀𝑛𝑛.𝑢𝑙𝑡𝑐𝑟 as shown in Figure 4.12.
Figure 4.12 Nonlinear tension softening [Hordijk et al., 1987]
Fracture energy Gf is estimated according to Equation (4.5) as specified in CEB-FIP
Model Code [1990] which provides relationship between compressive strength and fracture
energy. The fracture energy is related to both the compressive strength 𝑓𝑐𝑚 and the maximum
aggregate size dmax. The relationship according to the Model Code is:
𝐺𝑓 = 𝐺𝑓0 (𝑓𝑐𝑚
𝑓𝑐𝑚0)
0.7
(4.5)
with 𝑓𝑐𝑚0 equal to 10 MPa and the value of 𝐺𝑓0 related to the maximum aggregate size (Table
4.4). The maximum aggregate size used in concrete slabs is 12.5 mm, and thus the Gf0 value is
interpolated as 0.0275.
Table 4.4 Coefficient for determining fracture energy [MC 1990]
Maximum aggregate size,
dmax [mm]
Fracture energy,
Gf0[N/mm]
8 0.025
16 0.03
32 0.058
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In the smeared crack approach, the fracture zone is distributed in a certain width of the
finite element, which is designated crack band-width, h. The crack band-width must be mesh
dependent in order to ensure mesh objectivity [Sena-Cruz, 2004]. There are several different
ways to estimate h. In this study, the relationship ℎ = √2 × 𝐴 is used to estimated crack
bandwidth, where A is the area of a single element mesh.
4.2.1.4 Shear retention
When a crack occurs, the shear stiffness of the material is usually reduced. This
reduction is generally known as shear retention. DIANA offers two predefined relations for
shear retention: full shear retention and constant shear retention. The crack secant shear stiffness
is given by the general relation:
𝐷𝑠𝑒𝑐𝑎𝑛𝑡𝐼𝐼 =
𝛽
1 − 𝛽 𝐺 (4.6)
where G is the elastic shear modulus, β is the shear retention factor.
In case of full shear retention, the elastic shear modulus G is not reduced, and thus β =1
which implies that the secant crack shear stiffness is infinite. In case of constant shear retention,
the crack secant shear stiffness is reduced, the shear retention factor is in the range of 0 < β ≤
1. In this study, full shear retention is used in the model.
4.2.2 Steel Reinforcement
For embedded reinforcement, DIANA offers seven different material models [DIANA,
2015]. Among all the available material models, Von Mises plasticity and hardening model is
adopted for embedded reinforcement in the present study. Figure 4.13 illustrates the bilinear
stress strain relationship diagram for the embedded reinforcement. The yield stress fy and
ultimate stress fult are measured from the experimental testing of steels. The Young’s modulus
used in the finite element model for both Ø6 and Ø8 steels are not the ones determined from
the experimental testing, but assumed to be 200 GPa. The yield strain εy input in the model is
thus obtained from the stress-strain relationship. The ultimate strains εult for both types of steels
are assumed to be 0.1. The Poisson ratio is specified as 0.3 for the steel reinforcement. The
main properties for steel reinforcements are summarized in Table 4.5.
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Since 2-dimensional model is used to simulate 3-dimensional slab, the cross-sectional
areas of the steel reinforcement specified in material properties are the total cross-sectional
areas of the steel reinforcement. For instance, three Ø6 steel bars are used as upper longitudinal
reinforcement, and thus the cross-sectional areas assigned to it would be the total cross-sectional
areas of the three Ø6 steel bars. Therefore, for the same reason, the cross-sectional areas
assigned to lower longitudinal reinforcement are the total cross-sectional areas of five Ø8 steel
bars. The cross-sectional areas assigned to all shear reinforcement are two times the cross-
sectional area of a single Ø6 steel bar, except for the one at the mid span which has the cross-
sectional area of a single Ø6 steel bar due to the symmetry effect.
Figure 4.13 Bilinear stress-strain relationship for steel
Table 4.5 Summary of steel reinforcement model properties
Property Remarks DIANA syntax
Young’s modulus, Es 200 GPa YOUNG 2.00E+5
Poisson ratio 0.3 POISON 0.3
Reinforcement model Von Mises plasticity YIELD VMISES
Hardening model Bilinear HARDIA fy,d , εy,d, ful,d,0.1
However, in the initial analysis in which the yield stress fy and ultimate stress fult
obtained from the experimental results were used in the model, it was discovered that the finite
element model overestimated the results for total applied load versus deflection when
comparing with the experimental results. This is due to the fact that the stress-strain relationship
for a bare steel reinforcement is different from the average stress-strain relationship for steel
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reinforcement embedded in concrete. In another word, the averaged stress-strain relationship
for embedded steel reinforcement should have lower yield stress and ultimate stress than those
of a bare steel reinforcement. Therefore, to take into account for this fact, the yield envelope of
the bare steel reinforcement is reduced as illustrated in Figure 4.14, according to the expression
proposed by Stevens et al. [1987]:
𝛥𝜎𝑦𝑐𝑟 = 75
𝜙𝑠 𝑓𝑐𝑡 × 𝐶𝑏 (4.7)
where 𝜙𝑠 is the diameter of the steel reinforcement, 𝑓𝑐𝑡 is the tensile strength of concrete, and
𝐶𝑏 is the effective grip factor evaluated from Equation (4.6). A non-perfect grip case is
considered in this study.
𝐶𝑏 = {
1 (perfect grip)𝜏𝑏
5𝑓𝑐𝑡 , 𝜏𝑏 = 13.5 MPa (other cases)
(4.8)
Figure 4.14 The averaged stress-strain relationship for embedded steel reinforcement with
reduced yield envelope [Stevens et al., 1987]
4.2.3 Carbon Fiber Reinforcement Polymer (CFRP)
In this experimental work, the CFRP laminate strips consists of unidirectional carbon
fibers held together by epoxy vinyl ester resin matrix. The material property of CFRP laminate
was characterized and presented in Chapter 3. The Young’s modulus of CFRP laminate is 164
GPa. The cross sectional area is 60 mm2 with a length of 50 mm and a thickness of 1.2 mm.
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The behavior of CFRP laminate in all three directions is considered to be linear elastic. A
summary of the main properties of CFRP is shown in Table 4.6.
Table 4.6 Summary of CFRP material model properties
Property Remarks DIANA syntax
Young’s modulus, ECFRP 164 GPa YOUNG 164E+3
Cross sectional area 60 mm2 CROSSE 60
4.2.4 Concrete-CFRP Interface
Interface material model is one of the most difficult parts to be determined since there
was no experimental work carried out to characterize the interface material property. To
simulate the interface behavior in the present study, bond-slip model has been adopted among
all the available interface models offered by DIANA. In particular, a bilinear bond-slip law has
been proven to be suitable to model unidirectional interface element [Lu et al., 2005]. As shown
in Figure 4.15, the maximum bond stress τmax is reached at relative slip s0 before debonding
initiation occurs between CFRP and concrete substrate. The elastic stiffness D11 is obtained
from the initial slope before debonding point. After τmax is reached and debonding initiation
starts, the bond stress decreases linearly to 0 at ultimate slip smax. At this point, complete
debonding occurs.
In this study, the recommendation of initial slip at 0.05 mm and ultimate slip at 0.2 mm
by Lu et al. [2005] has been adopted. Several attempts were made to evaluate the maximum
bond strength τmax within the range of 4 MPa ~7 MPa. It has been found that a τmax value of 6
MPa best correlates the interface behavior in the finite element model with that of experimental
results. A summary of main properties for interface is shown in Table 4.7 below.
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Figure 4.15 The bond-slip model for unidirectional interface element [Lu et al. 2005]
Table 4.7 Summary of interface material model properties
Property Remarks DIANA syntax
Maximum bond strength 6 MPa -
Stiffness 110 MPa/mm DSTIF 110
Bond-slip Bi-linear law SLPVAL 0 0 6 0.05 0 0.2
4.3 Prestressing
The prestress has been applied as a temperature loading to CFRP in the model, following
the relationship in Equation (4.9)
𝜀𝑖𝑛𝑖 = 𝛼 × ∆𝑡 (4.9)
where 𝜀𝑖𝑛𝑖 is the initial strain measured in the prestressed CFRP, 𝛼 is the thermal expansion
coefficient of CFRP and assumed to be 1×10-5 ℃−1 and ∆𝑡 is the change in temperature. For
the RC slab strengthened with CFRP by mechanical anchorage, the initial strain measured in
the prestressed CFRP is 4.23 ×10-3. Thus, a temperature load of -423 ℃ is applied to all the
CFRP elements.
In addition, the temperature load which cannot be processed directly in a nonlinear
analysis, must be analyzed in the transient state in DIANA. As such, the temperature load is
applied at the beginning of the analysis as load case 1, followed by a deformation load as load
case 2. In this way, the prestress force is being applied to the CFRP elements first before the
nonlinear analysis is being processed.
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4.4 Mechanical Anchorage
For the case of MA, the prestressed CFRP laminates were fixed onto concrete by means
of mechanical anchor plates (with a geometry of 270 mm × 200 mm × 20 mm). The detailed
illustrations and procedures are described in Chapter 3. The length of the mechanical anchor
plate is 270 mm. Since there is no information about the effective length of such device, two
methods have been attempted to model the anchorage. The mechanical anchorage is simulated
by fixing the CFRP laminate to the concrete substrate: (i) over the length of anchor plate
(200~300 mm); or (ii) at a single extremity. From several trials, it has been discovered that a
single point anchorage best correlates the simulation results with experimental results.
The master-slave approach has been adopted to model the mechanical anchorage as a
single point constraint. In this method, the geometric point of the CFRP extremity is being
assigned as the “slave” and the corresponding geometric point on concrete as the “master”. The
master may have multiple degree of freedom (dof). The slave does not have its own dof, but can
follow the movement of the master in a specified dof. Then, the “slave” is being connected to
the “master” by introducing a single-point tying. In the MA case, only translation in x direction
is allowed for both master and slave during tying to ensure that no CFRP end debonding occurs.
4.5 Creep Model
Creep test has been simulated based on the existing FE model for the MA slab. The
creep model for concrete according to CEB-FIP Model Code 1990 has been adopted. The
critical parameters for creep modeling are summarized in Table 4.8. In order to account the
effect of prestressing in the strengthened slab, the FE model has been programmed to start the
creep test simulation from the time of prestressing application by introducing a time curve in
the analysis. Basically, the time curve depicts all the events throughout the time history during
creep test analysis: firstly, the prestress has been applied at time 0; then, a sustained load of 20
kN has been applied to the slab 172 days after prestressing; and this sustained load has remained
for 257 days until the load is removed at the end of the creep test. Since the total duration (about
257 days) of the analysis is considerably long, smaller time step is chosen only at the vicinity
of loading and unloading in order to save computation time.
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Table 4.8 Summary of creep model properties
Property Remarks DIANA syntax
Creep model CEB-FIP Model Code 1990 CONCRE MC1990
Concrete grade C30 GRADE C30
Young’s modulus 30.4 GPa YOUNG 3.04E+4
Ambient temperature 20 ºC TEMPER 20
Relative humidity 50% RH 50
Age at loading 250 days LODAGE 250
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CHAPTER 5 NUMERICAL SIMULATION RESULTS AND
DISCUSSIONS
5.1 Numerical Simulation for Monotonic Load Tests
The numerical simulation results for the monotonic loading tests are compared with
those obtained from experimental results. The following main aspects are compared: (i) load
vesus mid-span displacement; (ii) load vesus mid-span concrete strains; (iii) load vesus mid-
span CFRP strains; (iv) load vesus mid-span steel strains; and (v) crack patterns.
5.1.1 Load vs Mid-span Deflection
The comparisons between the experimental and numerical results of the applied load
and mid-span deflection relationship for all slabs are shown in Figure 5.1 to 5.3. Generally, the
curves depict three different stages of the slabs during loading, namely: (i) elastic phase —
before crack initiation of concrete; (ii) cracked phase — from concrete cracking until yield
initiation of steel reinforcement; and (iii) yielding phase — steel yielding until ultimate load
failure. Similar trends are observed between the numerical and experimental results, capturing
the key features during these stages for all slabs.
The numerical simulation gives accurate prediction of the deformation responses of
three slabs in the elastic range before initiation of cracks occur in concrete. For the case of REF
and EBR slabs, after concrete cracking, the numerical simulation still captures the key features
of the deformation response such as steel yielding and ultimate failure, but with slight
overestimation as compared to the experimental results. It is important to note that after cracks
occur in concrete, the steel reinforcements (for REF) and CFRP (for EBR and MA) have
become the main carrier of the applied load. The slight overestimation by numerical simulation
may be due to the fact that during finite element modelling stage, a perfect bond has been
assumed between the embedded steel reinforcements and concrete. In reality, there might be
slip at steel-concrete interface and this has not been considered in the model. Additionally, the
initial stress state due to the self-weight was not accounted for in the FE model.
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It is interesting to note that for the case of MA slab, the numerical simulation precisely
captures the intermediate debonding at about 55 kN with a horizontal curve shown in Figure
5.3. Since a linear elastic behavior is assumed for CFRP laminates, the ultimate load for MA
slab in the numerical simulation is determined by the rupture of CFRP which has a tensile
strength of 2375 MPa (see Chapter 3). The numerical simulation also captures the ultimate load
with relatively good accuracy.
Figure 5.1 Load vs mid-span deflection graph comparison for REF slab
0
5
10
15
20
25
30
35
40
0 20 40 60 80 100
Tota
l lo
ad, F
[kN
]
Mid-span displacement,ẟ [mm]
Exp-REFFEM-REF
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Figure 5.2 Load vs mid-span deflection graph comparison for EBR slab
Figure 5.3 Load vs mid-span deflection graph comparison for MA slab
0
10
20
30
40
50
60
0 20 40 60 80 100
To
tal
load
, F
[k
N]
Mid-span displacement,ẟ [mm]
Exp-EBR
FEM-EBR
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Tota
l lo
ad,
F [
kN
]
Mid-span displacement,ẟ [mm]
Exp-MA
FEM-MA
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5.1.2 Load vs Mid-span Concrete Strain
The comparisons between the experimental and numerical results of the applied load
and top mid-span top concrete strain relationship for all slabs are shown in Figure 5.4 to 5.6.
The strain results are obtained for the concrete at the mid-span compression surface. The
numerical and experimental results differ significantly, mainly in term of concrete strain values.
This is due to the fact that, a linearly constant compression function has been adopted to
describe the concrete behavior under compressive stress state. This compression function is
usually for ideal case in which a constant softening law is used after the compressive strength
of concrete is reached. It is worth pointing out that the numerical simulation agrees accurately
with the experimental results in the elastic phase before crack initiation.
Figure 5.4 Load vs mid-span concrete strain graph comparison for REF slab
0
5
10
15
20
25
30
35
0.0 0.5 1.0 1.5 2.0
Tota
l lo
ad, F
[kN
]
Mid-span top concret strain, εc [×10-3]
FEM-REF
Exp-REF
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Figure 5.5 Load vs mid-span concrete strain graph comparison for EBR slab
Figure 5.6 Load vs mid-span concrete strain graph comparison for MA slab
0
10
20
30
40
50
60
0.0 0.5 1.0 1.5 2.0
To
tal
load
, F
[k
N]
Mid-span top concret strain, εc [×10-3]
FEM-EBR
Exp-EBR
0
10
20
30
40
50
60
70
80
0.0 0.5 1.0 1.5 2.0
To
tal lo
ad, F
[kN
]
Mid-span top concret strain, εc [×10-3]
FEM-MA
Exp-MA
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5.1.3 Load vs Mid-span CFRP Strain
The comparisons between the experimental and numerical results of the applied load
and mid-span CFRP strain relationship for EBR and MA slabs are shown in Figure 5.7 and 5.8,
respectively. Similar trend of load versus mid-span CFRP strain curves are observed between
numerical and experimental results, with three distinct parts contributing to the overall curve
(similar to that for load versus mid-span deflection curve): (i) before crack initiation of concrete;
(ii) from concrete cracking until yield initiation of steel reinforcement; and (iii) from steel
yielding until ultimate load failure.
Before concrete crack initiation, the strain change in CFRP laminates is minimal. The
strain change in CFRP laminates becomes significant after concrete cracking occurs. Moreover,
for the MA case, initiation of concrete cracking happens at a higher applied load of about 20
kN as compared to that of EBR slab at about 10 kN. This could be due to the contribution of
the prestressed CFRP laminates as well as fixed mechanical anchorage system.
Figure 5.7 Load vs mid-span CFRP strain graph comparison for EBR slab
0
10
20
30
40
50
60
0 2 4 6 8
Tota
l fo
rce,
F [
kN
]
Mis-span CFRP strain,εCFRP [×10-3]
Exp-EBR
FEMEBR
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Figure 5.8 Load vs mid-span CFRP strain graph comparison for MA slab
5.1.4 Load vs Mid-span Longitudinal Steel Strain
It is important to monitor the strain evolution with the applied load for steel
reinforcement in tension. However, the strain of the bottom longitudinal steel reinforcement
(ϕ8) was not measured during the experiment due to the difficulty of implementation. The
numerical results of the applied load and mid-span bottom longitudinal steel reinforcement
strain relationship for all slabs are shown in Figure 5.9. The yield strain εy of the steel
reinforcement is approximately 2.5 ‰ and this value corresponds to a yield strength of 500
MPa which is close to the yield strength of the steel reinforcement used in the model after the
modification of reduced yield envelope (520 MPa). As such, the bottom steel reinforcement has
reached yielding point. Therefore, as expected, it can be easily seen that the strengthened RC
slabs (EBR and MA) reach higher loads when the steel reinforcement has yielded. Moreover,
similar strain response is observed for EBR and MA, with MA sustaining higher load than EBR
for the same strain level.
0
10
20
30
40
50
60
70
80
0 5 10
To
tal
forc
e, F
[k
N]
Mis-span CFRP strain,εCFRP [×10-3]
Exp-MA
FEM-MA
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Figure 5.9 Load vs mid-span steel strain graph from numerical simulations
5.1.5 Crack Patterns
The crack pattern of the tested slabs were monitored and recorded for the whole span
length as shown in Figure 5.10. The crack patterns from the final step of the numerical
simulations are illustrated in Figure 5.11 to 5.13 which only shows half span of the slabs. By
comparison, it can be concluded that the numerical simulation is able to predict the crack
patterns with relatively high accuracy. Generally, both experimental and numerical results show
that cracks locate at the tensile surface of the slabs near the proximity of the loading point.
Figure 5.10 Crack patterns of all slabs from experimental results
0
10
20
30
40
50
60
70
80
-0.5 0 0.5 1 1.5 2 2.5 3
Tota
l lo
ad, F
[kN
]
Mid-span bottom steel reinforcement strain, εc [×10-3]
FEM-REF
FEM-EBR
FEM-MA
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Figure 5.11 Crack patterns from numerical simulation-REF slab
Figure 5.12 Crack patterns from numerical simulation-EBR slab
Figure 5.13 Crack patterns from numerical simulation-MA slab
5.2 Numerical Simulation for Creep Test
The numerical simulation results of time evolution of mid-span deflection of the MA
slab for creep test are compared with the experimental results. Factors affecting the creep test
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are briefly discussed. Important simulation results such as prestress loss in CFRP laminate is
also presented.
5.2.1 Effects of Temperature and Relative Humidity
The comparison of time evolution of mid-span deflection of the MA slab between the
experimental and numerical results is presented in Figure 5.14. The FE model provides the
overall results with high accuracy for the long-term behavior of the MA slab during creep test.
However, it should be noted that there is a distinct overestimation for mid-span deflection by
the FE model before time reaches 75 days. In the actual experiment, the slab was only submitted
to the controlled environment (20 ºC and 50% RH) after 350 hours from the beginning of the
creep test. In addition, the creep test was carried out from 17-Dec-2014 onwards, which was
the winter season where the RH and the average ambient temperature were much lower than
the controlled environment (20ºC and 50% RH). Furthermore, for the first 350 hours, the slab
was subjected to laboratory environment which the daily temperature usually vary more than
10 ºC. These factors have not been considered in the numerical simulation. In the FE model, a
constant temperature of 20ºC and 50% RH is assumed in the simulation. Since creep increases
with increasing temperature [Bazant and Wittmann, 1982], this might be a possible explanation
for the distinct difference at the early stage of the creep test.
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Figure 5.14 Time evolution of mid-span deflection comparison for creep test
5.2.2 Loss of Prestress in CFRP
Since the FE model starts the creep modelling from the day of prestressing application,
it is important to check the prestress loss till the day of creep test. As such, the numerical results
of time evolution of mid-span CFRP stress from the day of pretressing application till the day
of creep test which is a total period of 172 days is presented in Figure 5.15. The initial applied
prestress is 680 MPa, and the prestress gradually decreases to 650 MPa over 172 days. This
prestress loss corresponds to approximately 4% which is relatively negligible. Therefore, the
loss of prestress in CFRP laminate of the present strengthened RC slab is minimal.
0
2
4
6
8
10
12
14
0 50 100 150 200 250 300
Mid
-sp
an D
isp
lace
men
t [m
m]
Time [Day]
Exp-MAFEM-MA
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Figure 5.15 Time evolution of mid-span CFRP stress prior to creep test
5.3 Conclusions
In summary, the numerical simulation predicts the structural behaviors of the RC slabs
accurately, capturing the critical stages such as crack initiation, yielding and ultimate failure
with relatively high precision. A summary of these important parameters is presented in Table
5.1. Good agreement has been established between the experimental and numerical results. In
addition, the creep model developed based on existing FE model also correlates very well with
the experimental results, making the numerical simulation as a reliable tool to predict the long-
term behaviors of the CFRP strengthened RC slabs.
Table 5.1 Main summary of numerical simulation results
Stiffness Crack
Initiation Yielding Ultimate
KI KII ẟcr Fcr ẟy Fy ẟmax Fmax
[kN/mm] [kN/mm] [mm] [kN] [mm] [kN] [mm] [kN]
REF 11.71 0.52 1.11 13 18 26.2 100 30.2
EBR 9.17 1.34 1.2 11 20 36.2 39 48.2
MA 11.80 1.42 1.78 21 19.4 46 90.4 67.6
640
650
660
670
680
690
700
0 50 100 150
Mid
-span
CF
RP
str
ess,
[M
Pa]
Time [Day]
FEM-MA
650 MPa
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CHAPTER 6 PARAMETRIC STUDIES
6.1 Introduction
A series of parametric studies have been developed to investigate the influence of
important parameters defining the prestressed slab’s characteristics. A controlled slab is used
as the reference slab (REF-P) with its properties shown in Table 6.1. Since it has been proven
from the experimental results that the RC slab strengthened with CFRP laminate by MA shows
excellent performance in terms of overall structural behavior, the parametric studies is
developed based on the MA method. The objective of the parametric studies is to evaluate the
sensitivity of the REF-P slab with variations of the following three parameters: (i) prestress
level; (ii) concrete grade; and (iii) CFRP laminate geometry. For each group, two parameter
variations will be compared with that of REF-P. As such, prestress level at 0.6% and 0.8%,
concrete grade of C35/45 and C40/50, and CFRP laminate geometry of 80 × 1.2 and 100 × 1.2
will be studied. The CFRP laminate has the same Young’s modulus of elasticity and ultimate
tensile strength regardless of geometry.
Table 6.1 Summary of parameter variations for parametric studies
Prestress Concrete grade CFRP geometry
REF-P 0.4% C30/37 50 × 1.2
PR-0.6% 0.6% C30/37 50 × 1.2
PR-0.8% 0.8% C30/37 50 × 1.2
CG-C35/45 0.4% C35/45 50 × 1.2
CG-C40/50 0.4% C40/50 50 × 1.2
LG-80× 1.2 0.4% C30/37 80× 1.2
LG-100× 1.2 0.4% C30/37 100× 1.2
Note: C35/45 (fcm=43 MPa, Ec=34 GPa); C40/50 (fcm=48 MPa, Ec=35 GPa)
CFRP: E=170 GPa, fu=2500 MPa
6.2 Variation in Prestress Level
The comparison of load versus mid-span displacement for CFRP laminate with various
prestress level is illustrated in Figure 6.1. It is obvious that the prestress levels of CFRP laminate
significantly contribute to the load-displacement responses. A higher prestress level yields a
lower mid-span deflection at ultimate load, reducing the ductility of the slab. However, the
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effects of increasing prestress levels in CFRP laminate on the mid-span deflection at cracking
and yielding are not as significant as those on the ultimate loads. This phenomenon is due to
the fact that the total CFRP strains are fixed and thus the usable CFRP strains are decreased
when the initial prestress level is increased. Moreover, an increase of cracking and yielding
loads is observed with increasing prestress level in CFRP laminate. On the other hand, the
ultimate loads for the three slabs with different prestress levels are approximately the same,
implying that the prestress level does not contribute to the enhancement of the ultimate load
capacity of the strengthened slabs. This behavior is within the expectation since the failure of
the slab occurred by the tensile rupture of the CFRP laminate.
Figure 6.2 and 6.3 show the strain development for CFRP, concrete and steel at mid-
span with various prestress levels of CFRP laminate, respectively. There is no significant strain
changes in the prestressed CFRP laminate (Figure 6.2) and steel reinforcement (Figure 6.3)
until cracking. However, the influence of CFRP prestress levels on strain increment has become
considerably remarkable after cracking, and such influence becomes especially obvious after
yielding. As expected, as the applied load increases, the CFRP strains converge to
approximately the same ultimate strain value for different prestress levels. This phenomenon
provides an explanation for the similar ultimate failure loads observed in Figure 6.1. In
summary, an increase in prestress level of CFRP laminate contributes to a greater load capacity
at cracking and yielding, however, it does not affect the ultimate load capacity. Furthermore, a
higher prestress level in CFRP laminate yields a lower ultimate mid-span deflection and
consequently reduces the ductility, but has minimal effect on the deflection at cracking and
yielding.
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Figure 6.1 Load vs mid-span deflection graph comparison for variation of prestress levels
Figure 6.2 Load vs mid-span CFRP strain graph comparison for variation of prestress levels
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Tota
l lo
ad, F
[kN
]
Mid-span displacement,ẟ [mm]
REF-0.4%
PR-0.6%
PR-0.8%
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16
Tota
l fo
rce,
F [
kN
]
Mis-span CFRP strain,εCFRP [×10-3]
REF-0.4%PR-0.6%PR-0.8%
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Figure 6.3 Load vs mid-span concrete and steel strain graph comparison for variation of
prestress levels
6.3 Variation in Concrete Grade
The comparison of load versus mid-span displacement for CFRP strengthened slabs
with various concrete grades is illustrated in Figure 6.4. Figure 6.5 and 6.6 shows the strain
development for CFRP, concrete and steel at mid-span with various concrete grades,
respectively. Similar trend in load-deflection response is observed for the slabs with three
different concrete grades, except for the distinct intermediate debonding behaviors. The strain
development for CFRP and steel at mid-span is not affected significantly by variation of
concrete grades as shown by Figure 6.5 and 6.6. Therefore, it can be concluded that by changing
the concrete grades from C30/37 to C35/45 and C40/50, the enhancement in load capacity at
cracking, yielding and ultimate failure is not significantly affected. It should be stressed that
the variation of concrete grade mainly affected the tensile response of this material since under
compression, in all the simulations a linear elastic behavior was assumed. This assumption was
adopted since in the experiments crushing of the concrete under compressive forces was never
experienced.
0
10
20
30
40
50
60
70
80
-2 -1 0 1 2 3
Tota
l lo
ad, F
[kN
]
Mid-span concrete and steel strain, ε [×10-3]
REF-0.4%PR-0.6%PR-0.8%SteelConcrete
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Figure 6.4 Load vs mid-span deflection graph comparison for variation of concrete grade
Figure 6.5 Load vs mid-span CFRP strain graph comparison for variation of concrete grade
0
10
20
30
40
50
60
70
80
0 20 40 60 80 100
Tota
l lo
ad, F
[kN
]
Mid-span displacement,ẟ [mm]
REF-C35/37
CG-C35/45
CG-C40/50
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16
Tota
l fo
rce,
F [
kN
]
Mis-span CFRP strain,εCFRP [×10-3]
REF-C30/37
CG-C35/45
CG-C40/50
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Figure 6.6 Load vs mid-span concrete and steel strain graph comparison for variation of
concrete grade
6.4 Variation in CFRP Laminate Geometry
The comparison of load versus mid-span displacement for CFRP strengthened slabs
with various CFRP laminate geometry is illustrated in Figure 6.7. Figure 6.8 and 6.9 shows the
strain development for CFRP, concrete and steel at mid-span of the slabs with various CFRP
laminate geometry, respectively. It clearly demonstrates the significance of the CFRP laminate
geometry on the load-deflection (Figure 6.7). Generally, a larger cross-sectional area of the
CFRP laminate contributes to a greater load capacity at all critical stages, being cracking,
yielding and ultimate failure. This benefit is especially obvious at ultimate failure with
approximately 38% and 63% increase in ultimate load capacity for LG-80×1.2 and LG-
100×1.2, respectively, as compared to REF-50×1.2. As shown in Figure 6.8, the slabs
strengthened with different CFRP laminate geometry reach the same ultimate CFRP strain,
however, slabs strengthened with larger cross-sectional CFRP laminate area bear higher
ultimate failure load. Therefore, it can be concluded that a larger cross-sectional area of CFRP
laminate contributes to an increase in load capacity at cracking, yielding and especially ultimate
failure.
0
10
20
30
40
50
60
70
80
-2 -1 0 1 2 3
Tota
l lo
ad, F
[kN
]
Mid-span concrete and steel strain, ε [×10-3]
REF-C30/37
CG-C35/45
CG-C40/50Concrete Steel
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Figure 6.7 Load vs mid-span deflection graph comparison for variation of CFRP geometry
Figure 6.8 Load vs mid-span CFRP strain graph comparison for variation of CFRP geometry
0
20
40
60
80
100
120
0 20 40 60 80 100
Tota
l lo
ad, F
[kN
]
Mid-span displacement,ẟ [mm]
REF-50×1.2LG-80×1.2LG-100×1.2
0
20
40
60
80
100
0 2 4 6 8 10 12 14 16
Tota
l fo
rce,
F [
kN
]
Mis-span CFRP strain,εCFRP [×10-3]
REF-50×1.2
LG-80×1.2
LG-100×1.2
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Figure 6.9 Load vs mid-span concrete and steel strain graph comparison for variation of
CFRP geometry
6.5 Summary
The important simulation results from parametric studies are summarized in Table 6.2
below. Figure 6.10 and 6.11 further illustrates the effects of variation of different parameters
on total applied load and mid-span deflection, respectively. Critical aspects such as crack
initiation, yielding and ultimate failure are depicted. Moreover, the stiffness at elastic uncracked
phase (KI) and after cracking (KII) are also compared in Figure 6.12. The influence of variation
of different parameters on KI is significant whereas after cracking occurs, the stiffness (KII)
becomes unaffected by such variations. The following conclusions can be made from
parametric studies:
(i) Prestress level of CFRP laminate: an increase in prestress level from 0.4% to 0.6%
and 0.8% respectively provides significant enhancement of load capacity at crack
initiation and yielding, but not at ultimate failure load. On the other hand, the increase
in prestress level does not affect the mid-span deflection at crack initiation and yielding,
whereas it results in a significant reduction in mid-span deflection at ultimate failure. In
0
20
40
60
80
100
120
-2 -1 0 1 2 3
Tota
l lo
ad, F
[kN
]
Mid-span concrete and steel strain, ε [×10-3]
REF-50×1.2LG-80×1.2LG-100×1.2Concrete Steel
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addition, the stiffness at elastic phase (KI) is increased with higher prestress level of
CFRP laminate.
(ii) Concrete grade: an increase of concrete grade (and thus the compressive strength and
modulus of elasticity) from C30/37 to C35/45 and C40/50 respectively provides
minimal enhancement in terms of load capacity and mid-span deflection. A marginal
increment of KI is observed with an increase in concrete grades.
(iii) CFRP laminate geometry: an increase of CFRP laminate cross-sectional area from 50
× 1.2 to 80 × 1.2 and 100× 1.2 respectively results in a significant increment of load
capacity at crack initiation and yielding, and such enhancement becomes considerably
remarkable at ultimate failure. On the other hand, the mid-span deflection at all critical
stages (crack initiation, yielding and ultimate failure) is not affected by the variation of
laminate geometry. Furthermore, the increase in KI is significant with larger cross-
sectional area of CFRP laminate.
Table 6.2 Main summary of results from parametric studies
Stiffness
Crack
Initiation Yielding Ultimate
KI KII ẟcr Fcr ẟy Fy ẟmax Fmax [kN/mm] [kN/mm] [mm] [kN] [mm] [kN] [mm] [kN]
REF-P 9.87 1.41 2.23 22.0 33.7 52.6 93.4 69.4
PR-0.6% 14.08 1.53 1.79 25.2 30.8 60.0 76.6 68.2
PR-0.8% 15.44 1.54 1.93 29.8 30.5 64.6 60.3 67.6
CG-C35/45 10.67 1.43 2.10 22.4 39.3 60.0 92.9 68.6
CG-C40/50 10.98 1.43 2.04 22.4 30.5 54.6 97.3 71.0
LG-80x1.2 14.75 1.75 1.79 26.4 29.9 68.0 92.7 90.8
LG-100x1.2 15.89 1.95 1.90 30.2 28.2 75.6 97.7 108.0
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Figure 6.10 Load variation for slabs from parametric studies
Figure 6.11 Mid-span deflection variation for slabs from parametric studies
0
20
40
60
80
100
120
Tota
l fo
rce,
F [
kN
]CrackingYieldingUltimate
0
20
40
60
80
100
120
Mid
-span
def
lect
ion,
ẟ [
mm
]
CrackingYieldingUltimate
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Figure 6.12 Stiffness variation for slabs from parametric studies
0
5
10
15
20
Sti
ffnes
s, K
[kN
/mm
]
KI
KII
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CHAPTER 7 CONCLUSIONS AND RECOMMENDATIONS
7.1 Conclusions from Present Study
The objectives of this study has been achieved. FE models have been developed to
simulate numerically the experimental results of the prestressed slabs tested up to the failure
and under sustained loads (creep test). By comparisons of the relevant results, good correlations
have been found between the numerical and experimental results. Since the existing FE models
predict the structural behavior of the slabs with high accuracy, parametric studies have been
performed based on these models to analyse the effect of relevant variables, such as prestressing
level, concrete grade and CFRP laminate geometry.
Several conclusions can be drawn from this study. The performance of RC slabs
strengthened with CFRP (both prestressed and non-prestressed) are significantly improved in
terms of lower deflection, crack width delay and lower crack spacing. In addition, the metallic
anchors composing the MA system prevented a premature failure by debonding and allowed
the slabs to support higher ultimate loads and deflections. A greater use of the CFRP laminate
strip tensile capacity was attained when prestressing was applied to the CFRP laminates. The
average ultimate strain on the CFRP laminate increased by 74% with prestressing for the slabs
tested. Furthermore, the initial loss of prestress in CFRP laminate is relatively negligible,
making it a promising strengthening material.
From parametric studies, several conclusions can be summarized based on this study.
An increase in prestress level provides significant enhancement of load capacity at crack
initiation and yielding, and a significant reduction in mid-span deflection at ultimate failure.
The variation of concrete grade results minimal enhancement in terms of load capacity and mid-
span deflection. By increasing the cross-sectional area of CFRP laminate, the load capacity at
crack initiation and yielding is significantly increased, and such enhancement becomes
considerably remarkable at ultimate failure.
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7.2 Recommendations for Future Work
Based on this study, several recommendations are suggested for future work in the area
of structural behaviors of RC slabs strengthened with prestressed CFRP laminates. The long-
term behavior of the strengthened slabs can be further explored in depth. From this study, it has
been concluded that the existing FE model provides an accurate simulation as the experimental
creep tests. Future work in the area of FEM simulation of long-term behavior of the
strengthened slabs, taking into account the temperature influence can be developed. In addition,
the viscoelastic effects of prestressed CFRP can also be explored thoroughly. Furthermore, the
durability of the strengthened slabs when subjected to extreme temperatures or harsh
environment is also an interesting research area.
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